Title: Unit 6 Quiz
Course: Technical Math for Industry

Q: Determine the number of solutions you will have for the system and
- One solution. (Correct. Rearranging the equations into , you see that the lines have different slopes and therefore must intersect at one point.)
- Indefinite solutions. (Incorrect. Rearrange the equations into form. Are the slopes of the lines the same or different? What does that mean?)
- Impossible to determine. (Incorrect. Rearrange the equations into form. Are the slopes of the lines the same or different? What does that mean?)
- No solutions. (Incorrect. Rearrange the equations into form. Are the slopes of the lines the same or different? What does that mean?)
A: One solution.

Q: Determine the number of solutions the system of and will have.
- Infinite solutions. (Correct. Rearranging the equations into , you see that the lines are exactly the same and therefore have infinitely many solutions.)
- No solutions. (Incorrect. Rearrange the equations into form. What do you notice? Can you think of more than one set of values for x and y that would solve both equations?)
- One solution. (Incorrect. Rearrange the equations into form. What do you notice? Can you think of more than one set of values for x and y that would solve both equations?)
- Impossible to determine. (Incorrect. Rearrange the equations into form. What do you notice? Can you think of more than one set of values for x and y that would solve both equations?)
A: Infinite solutions.

Q: Which of the following can be solved by using a system of equations?
- Laura and Mark went to the movies and spent $29 on movie tickets and snacks. Popcorn cost $5. How much were the tickets? (Incorrect. There is not enough information to solve this problem. Snacks could be more than just popcorn.)
- Laura and Mark went to the movies and spent $29 on movie tickets and snacks.  The tickets cost $9.75 per person.  How much money did they spend on snacks? (Incorrect. A system of equations is not needed to solve the problem. The equation will solve for the price of a ticket.)
- Laura and Mark went to the movies and spent $29 on movie tickets and snacks.  If they spent $8.50 on snacks, how much did the tickets cost? (Incorrect. A system of equations is not needed to solve the problem. The equation will solve for the price of a ticket.)
- Laura and Mark went to the movies and spent $29 on movie tickets and snacks.  Mark paid $10 more than Laura.  How much did each spend? (Correct. This problem can be solved by the system and where where l represents the amount of money that Laura spent, and m represents the amount of money that Mark spent.)
A: Laura and Mark went to the movies and spent $29 on movie tickets and snacks.  Mark paid $10 more than Laura.  How much did each spend?

Q: In yesterday's basketball game, Emily scored 19 points with a combination of 2-point and 3-point baskets. She scored a total of 9 baskets.

Which graph below accurately models this situation?

Note: In all graphs below, the x-axis represents 2-point baskets and the y-axis represents 3-point baskets.
A: (a choice with no text)
If wrong: Incorrect. Think about the relationships between the number of 2-point and 3-point baskets made. The total number of baskets is given by the equation ; which graphs include this line?
If wrong: Incorrect. Think about the relationships between the number of 2-point and 3-point baskets made. The total number of baskets is given by the equation ; which graphs include this line?
If wrong: Incorrect. Think about the relationships between the number of 2-point and 3-point baskets made. The total number of baskets is given by the equation ; which graphs include this line?
If right: Correct. This graph accurately shows the system and .

Q: In the graph below, the two lines intersect at (1, 1).

Which of the following systems of equations does the graph represent?
- and (Incorrect. For this to be the graph of the system, the equations of both lines have to be represented. Graph the two equations by making a table of values. Does the point (1, 1) satisfy both equations in the answer you chose?)
- and (Correct. This graph shows the system and .)
- and (Incorrect. For this to be the graph of the system, the equations of both lines have to be represented. While the line does go through the point (1, 1), is this the line shown on the graph?)
- and (Incorrect. For this to be the graph of the system, the equations of both lines have to be represented. While the line does go through the point (1, 1), is this the line shown on the graph?)
A: and

Q: Use the substitution method to determine whether the system of equations has one solution, no solution, or infinitely many solutions.
- The system has no solution; the lines are parallel. (Incorrect. Try rearranging the equations to compare the slopes and y-intercepts. What happens if you substitute in for x in the first equation? What does that mean?)
- It is impossible to determine from the information given. (Incorrect. Try rearranging the equations to compare the slopes and y-intercepts. What happens if you substitute in for x in the first equation? What does that mean?)
- The system has one solution; the two equations intersect at one point. (Incorrect. Try rearranging the equations to compare the slopes and y-intercepts. What happens if you substitute in for x in the first equation? What does that mean?)
- The system has infinitely many solutions; the two equations are the same line. (Correct. If you rearrange the equations and solve for y, you will see that they have the same slope and the same y-intercepts; therefore the lines are the same and the system will have infinitely many solutions.)
A: The system has infinitely many solutions; the two equations are the same line.

Q: Solve the system of equations using substitution.
A: (a choice with no text)
If wrong: Incorrect. Try substituting into the top equation for y. Solve for x. Use that x value in either equation to solve for y.
If wrong: Incorrect. Try substituting into the top equation for y. Solve for x. Use that x value in either equation to solve for y.
If wrong: Incorrect. Try substituting into the top equation for y. Solve for x. Use that x value in either equation to solve for y.
If right: Correct. When and , both equations are true. This means it is the solution of the system.

Q: Solve the system of equations using substitution.
A: (a choice with no text)
If right: Correct. When and , both equations are true. This means it is the solution of the system.
If wrong: Incorrect. Try substituting into the top equation for y. Don't forget to distribute the 8. Solve for x. Use that x value in either equation to solve for y.
If wrong: Incorrect. Try substituting into the top equation for y. Don't forget to distribute the 8. Solve for x. Use that x value in either equation to solve for y.
If wrong: Incorrect. Try substituting into the top equation for y. Don't forget to distribute the 8. Solve for x. Use that x value in either equation to solve for y.

Q: Rachel and Sam stopped at the donut stop before work. Rachel bought a protein smoothie and 2 boxes of donut holes for $11.65. Sam bought 2 protein smoothies and 1 box of donut holes for $10.55.

Use the substitution method to solve a system of equations relating S, the cost of a smoothie, and D, the cost of a box of donut holes.

How much does each item cost?
- Smoothie $3.15; box of donut holes $4.25 (Correct. Solving this system of equations by substitution method, you find that a smoothie costs $3.15 and a box of donut holes costs $4.25.)
- Smoothie $3.70; box of donut holes $3.70 (Incorrect. One way to solve the system is to first solve the top equation for S by subtracting 2D from both sides. The substitute the resulting expression into the bottom equation to solve for D.)
- Smoothie $4.25; box of donut holes $3.15 (Incorrect. One way to solve the system is to first solve the top equation for S by subtracting 2D from both sides. The substitute the resulting expression into the bottom equation to solve for D.)
- Smoothie $2.95; box of donut holes $4.35 (Incorrect. One way to solve the system is to first solve the top equation for S by subtracting 2D from both sides. The substitute the resulting expression into the bottom equation to solve for D.)
A: Smoothie $3.15; box of donut holes $4.25

Q: Solve the system of equations for x and y.
- (10, 5) (Incorrect. Substitute for y in the bottom equation and then solve the new equation for x.)
- (4, 9) (Incorrect. Substitute for y in the bottom equation and then solve the new equation for x.)
- (9, 4) (Incorrect. Substitute for y in the bottom equation and then solve the new equation for x.)
- (5, 10) (Correct. When and , both equations are true.)
A: (5, 10)

Q: Use the elimination method to solve the system for x and y.
A: (a choice with no text)
If wrong: Incorrect. Adding the two equations together eliminates the variable y to create the equation , so . What is the value of y?
If wrong: Incorrect. Adding the two equations together eliminates the variable y to create the equation , so . What is the value of y?
If wrong: Incorrect. Adding the two equations together eliminates the variable y to create the equation , so . What is the value of y?
If right: Correct. The point is a solution to both equations, and therefore is the solution to the system.

Q: Ivan and Jennifer went to the local deli to pick up sandwiches for the girls and boys soccer teams. Ivan ordered 10 roast beef subs and 8 Italian subs for a total of $89. Jennifer ordered 6 roast beef subs and 5 Italian subs for a total of $54.35.

One way to represent this situation is given in the system of equations below, where r represents the price of a roast beef sub, and i represents the price of an Italian sub.

Use the elimination method to figure out the price of each sandwich.
- roast beef sub $5.10; Italian sub $4.75 (Correct. If a roast beef sub costs $5.10 and an Italian sub costs $4.75, then both equations are true so this is the solution to the system.)
- roast beef sub $5.45; Italian sub $4.30 (Incorrect. Multiply the first equation by 5 and multiply the second equation by 8. Subtract them to eliminate the variable i and solve for r.)
- roast beef sub $5.00; Italian sub $4.85 (Incorrect. Multiply the first equation by 5 and multiply the second equation by 8. Subtract them to eliminate the variable i and solve for r.)
- roast beef sub $5.50; Italian sub $4.25 (Incorrect. Multiply the first equation by 5 and multiply the second equation by 8. Subtract them to eliminate the variable i and solve for r.)
A: roast beef sub $5.10; Italian sub $4.75

Q: Use the elimination method to solve the system for x and y.
A: (a choice with no text)
If wrong: Incorrect. Try multiplying the top equation by 2 and then adding the equations to eliminate the y variable.
If right: Correct. The the point is a solution to both equations, and therefore is the solution to the system.
If wrong: Incorrect. Try multiplying the top equation by 2 and then adding the equations to eliminate the y variable.
If wrong: Incorrect. Try multiplying the top equation by 2 and then adding the equations to eliminate the y variable.

Q: Use the elimination method to solve the system for x and y.
A: (a choice with no text)
If wrong: Incorrect. Rearrange the bottom equation so that it is in standard form, and then multiply it by 2. Eliminate the y variable and then solve for x.
If wrong: Incorrect. Rearrange the bottom equation so that it is in standard form, and then multiply it by 2. Eliminate the y variable and then solve for x.
If right: Correct. The point is a solution to both equations, and therefore is the solution to the system.
If wrong: Incorrect. Rearrange the bottom equation so that it is in standard form, and then multiply it by 2. Eliminate the y variable and then solve for x.

Q: Use the elimination method to solve the system for x and y.
A: (a choice with no text)
If wrong: Incorrect. Rearrange the bottom equation so that it is in standard form. Multiply the top equation by 2 and the bottom equation by 7, and then add. This eliminates the y variable. Solve for x.
If wrong: Incorrect. Rearrange the bottom equation so that it is in standard form. Multiply the top equation by 2 and the bottom equation by 7, and then add. This eliminates the y variable. Solve for x.
If wrong: Incorrect. Rearrange the bottom equation so that it is in standard form. Multiply the top equation by 2 and the bottom equation by 7, and then add. This eliminates the y variable. Solve for x.
If right: Correct. The point is a solution to both equations, and therefore is the solution to the system.

Q: Two trains leave stations 40 miles apart at the same time heading toward one another on parallel tracks. Train A is traveling 45 miles per hour, while Train B is going 65 miles per hour. The dispatcher wonders how long it will take them to meet each other.

Identify a system of equations can you use to solve this problem for t, the time it will take for the trains to pass each other.
- Train A: | Train B: (Incorrect. Using the formula d=rt, you can create a chart that generates the system of equations: | Distance | = | Rate | * | Time Train A | | = | 45 | * | t Train B | | = | 65 | * | t The rates of Trains A and B have been added in here. What values would you put in for the distances of the two trains? What system do you get when you do that?)
- Train A: | Train B: (Incorrect. Using the formula d=rt, you can create a chart that generates the system of equations: | Distance | = | Rate | * | Time Train A | | = | 45 | * | t Train B | | = | 65 | * | t The rates of Trains A and B have been added in here. What values would you put in for the distances of the two trains? What system do you get when you do that?)
- Train A: | Train B: (Incorrect. Using the formula d=rt, you can create a chart that generates the system of equations: | Distance | = | Rate | * | Time Train A | | = | 45 | * | t Train B | | = | 65 | * | t The rates of Trains A and B have been added in here. What values would you put in for the distances of the two trains? What system do you get when you do that?)
- Train A: | Train B: (Correct. By setting up this system of equations, you will be able to solve for t, the amount of time it will take the trains to pass each other. Since the trains are 40 miles apart, they will meet somewhere in the middle of the two stations. If Train A travels d distance then Train B will need to travel a distance of 40 – d so that the total distance traveled for the two trains is 40 miles, the distance that stations are apart from each other.)
A: Train A: | Train B:

Q: Two trains leave stations 75 miles apart at the same time heading toward one another on parallel tracks. Train A is traveling 60 miles per hour, while Train B is going 65 miles per hour.

How long after departure do the trains pass each other?
- 36 minutes (Correct. You can use this system to solve the problem for t, time: Solving for t by either substitution or elimination gives t = 0.6 (in hours), which is 36 minutes.)
- 126 minutes (Incorrect. You can use this system to solve the problem for t, time: Now use either the substitution or elimination method to solve for t. What do you find? (Remember that t will be in terms of hours, not minutes!))
- 12.5 minutes (Incorrect. You can use this system to solve the problem for t, time: Now use either the substitution or elimination method to solve for t. What do you find? (Remember that t will be in terms of hours, not minutes!))
- 60 minutes (Incorrect. You can use this system to solve the problem for t, time: Now use either the substitution or elimination method to solve for t. What do you find? (Remember that t will be in terms of hours, not minutes!))
A: 36 minutes

Q: A cross-country skier leaves her home at noon. She skis for an hour with the wind at her back, and then decides to turn around and take the same route home. Now that she is headed into the wind, her speed is 3 miles per hour slower going home than it was in the first hour. She arrives home at 3:30. She wondered how far away she was when she decided to turn back.

Which of these systems of equations can you use to solve this problem?
- Outgoing trip:

Incoming trip: (Incorrect. Use the formula to represent both legs of the journey: | Distance | = | Rate | * | Time Outgoing | d | = | r | * | Incoming | d | = | | * | 2.5 The distance, d, is the same in both trips because she took the same path home as she did on the way out. Think about the amount of time she spent on the outgoing journey. Is that information provided in the problem? Now think about the rate for her outgoing and incoming trips. If you represent her rate as r on the way out, how do you represent the idea of "3 miles per hour slower going home"? Which system represents the rates of the different parts of her trip correctly?)
- Outgoing trip:

Incoming trip: (Incorrect. Use the formula to represent both legs of the journey: | Distance | = | Rate | * | Time Outgoing | d | = | r | * | Incoming | d | = | | * | 2.5 The distance, d, is the same in both trips because she took the same path home as she did on the way out. Think about the amount of time she spent on the outgoing journey. Is that information provided in the problem? Now think about the rate for her outgoing and incoming trips. If you represent her rate as r on the way out, how do you represent the idea of "3 miles per hour slower going home"? Which system represents the rates of the different parts of her trip correctly?)
- Outgoing trip:

Incoming trip: (Incorrect. Use the formula to represent both legs of the journey: | Distance | = | Rate | * | Time Outgoing | d | = | r | * | Incoming | d | = | | * | 2.5 The distance, d, is the same in both trips because she took the same path home as she did on the way out. Think about the amount of time she spent on the outgoing journey. Is that information provided in the problem? Now think about the rate for her outgoing and incoming trips. If you represent her rate as r on the way out, how do you represent the idea of "3 miles per hour slower going home"? Which system represents the rates of the different parts of her trip correctly?)
- Outgoing trip:

Incoming trip: (Correct. Use the formula to represent both legs of the journey. Her outgoing trip can be represented by , and her incoming trip can be represented by , since her rate was 3 mph slower on the return trip.)
A: Outgoing trip:

Incoming trip:

Q: The field hockey team is holding several fundraisers to save up enough money to buy team jackets. Babysitting earns $6 per hour more than washing cars. Together the team worked 8 hours washing cars and 25 hours babysitting and earned a total of $414.

Which system of equations best represents the situation above?

Note: In all of the choices below, e represents money earned, r represents rate, and t represents time.
A: (a choice with no text)
If right: Correct. This system accurately represents the situation.
If wrong: Incorrect. The first equation can be interpreted "The team washed cars for 8 hours and earned $414." Is this a true statement? Do we know exactly how much they earned?
If wrong: Incorrect. The second equation can be interpreted "The team babysat for (25 - 8) hours." Is this a true statement? How long, in total, did they babysit?
If wrong: Incorrect. The top equation must represent washing cars, since . The expression means that the rate of washing cars is $6 more than the rate of babysitting, not the other way around.

Q: The art club is selling their handmade jewelry to raise money for new paints and brushes. Earrings were sold for $6 a pair and necklaces were sold for $12.50 each. They sold a total of 30 items and made $264.50.

Which system of equations best represents the situation above?

Note: In all of the choices below, e represents money earned, p represents price, and n represents number of items sold.
- Earrings:

Necklaces: (Correct. This system correctly relates the price of each item, the number sold, and the total amount of money earned.)
- Earrings:

Necklaces: (Incorrect. Where is the price of each item accounted for in this system?)
- Earrings:

Necklaces: (Incorrect. Look at the price of earrings and necklaces in this system. Is that consistent with the information provided in the problem?)
- Earrings:

Necklaces: (Incorrect. The top equation contains the expression to represent the number of earrings sold. If you sold 10 necklaces, how many earrings would you sell, accoring to this expression? Does that seem correct?)
A: Earrings:

Necklaces:

Q: Look at the table below.

 | Total $ |  | Price |  | Number sold
Bus Pass | $ | = | $75.00 | * |
Subway Pass | $ | = | $125.00 | * |
Total | $10,250 | = |  |  | 90

Which of the following scenarios could this table represent?
- Commuters in a city can purchase either a monthly Bus Pass or a monthly Subway Pass. The Bus Pass costs $75, and the Subway Pass costs $125. Last month, the city transit authority sold passes total. They earned $  from these sales. (Incorrect. Look at the table again. What is the total number of tickets sold? Is it , or do you know the actual number?)
- Commuters in a city can purchase either a monthly Bus Pass or a monthly Subway Pass. The Bus Pass costs $75, and the Subway Pass costs $125. Last month, the city transit authority sold x passes total. They earned $  from these sales. (Incorrect. Look at the table again. Find the total number of tickets sold and the total amount that the transit authority earned.)
- Commuters in a city can purchase either a monthly Bus Pass or a monthly Subway Pass. The Bus Pass costs $75, and the Subway Pass costs $125. Last month, the city transit authority sold 90 passes total. They earned $10,250 from these sales. (Correct. This answer choice could accurately represent the table provided.)
- Commuters in a city can purchase either a monthly Bus Pass or a monthly Subway Pass. The Bus Pass costs $125, and the Subway Pass costs $75. Last month, the city transit authority sold 90 passes total. They earned $10,250 from these sales. (Incorrect. Look at the prices for the passes. Do they match the information in the table?)
A: Commuters in a city can purchase either a monthly Bus Pass or a monthly Subway Pass. The Bus Pass costs $75, and the Subway Pass costs $125. Last month, the city transit authority sold 90 passes total. They earned $10,250 from these sales.

Q: How many pounds of walnuts that cost $7.60 per pound must be mixed with 6 pounds of cashews that costs $12 per pound to make a mixture of nuts that costs $9.25 per pound?
- 12 pounds (Incorrect. Use a chart to create an equation to solve the problem. You want to know the amount of walnuts, so label that x: | Total cost ($) | = | Price ($/pound) | * | Amount (pounds) Walnuts | | = | 7.60 | * | Cashews | 72.00 | = | 12.00 | * | 6 Total Mix | | = | 9.25 | * | Create an equation that relates the Total Costs, and solve for x.)
- 10.5 pounds (Incorrect. Use a chart to create an equation to solve the problem. You want to know the amount of walnuts, so label that x: | Total cost ($) | = | Price ($/pound) | * | Amount (pounds) Walnuts | | = | 7.60 | * | Cashews | 72.00 | = | 12.00 | * | 6 Total Mix | | = | 9.25 | * | Create an equation that relates the Total Costs, and solve for x.)
- 8 pounds (Incorrect. Use a chart to create an equation to solve the problem. You want to know the amount of walnuts, so label that x: | Total cost ($) | = | Price ($/pound) | * | Amount (pounds) Walnuts | | = | 7.60 | * | Cashews | 72.00 | = | 12.00 | * | 6 Total Mix | | = | 9.25 | * | Create an equation that relates the Total Costs, and solve for x.)
- 10 pounds (Correct. You need 10 pounds of walnuts for this mixture.)
A: 10 pounds

Q: Identify the chart that accurately displays the information and will help you solve the problem.

How many pounds of walnuts (cost: $7.60 per pound) must be mixed with 6 pounds of cashews (cost: $12 per pound) to make a mixture of nuts that costs $9.25 per pound?
-  | Total cost ($) | = | Price ($/pound) | * | Amount (pounds)
Walnuts |  | = | 7.60 | * |
Cashews | 72.00 | = | 12.00 | * | 6
Total Mix |  | = | 9.25 | * | (Incorrect. 6x is not the amount of pounds in the total mix. If you are adding x pounds and 6 pounds, how much is that?)
-  | Total cost ($) | = | Price ($/pound) | + | Amount (pounds)
Walnuts |  | = | 7.60 | + |
Cashews | 18 | = | 12.00 | + | 6
Total Mix |  | = | 9.25 | + | (Incorrect. To find the total cost you multiply the price per pound by the number of pounds. In this table, the values are being added.)
-  | Total cost ($) | = | Price ($/pound) | * | Amount (pounds)
Walnuts |  | = | 7.60 | * |
Cashews | 72.00 | = | 12.00 | * | 6
Total Mix |  | = | 9.25 | * | (Correct. The chart accurately displays the information and will solve the problem.)
-  | Total cost ($) | = | Price ($/pound) | * | Amount (pounds)
Walnuts | 45.60 | = | 7.60 | * | 6
Cashews |  | = | 12.00 | * |
Total Mix |  | = | 9.25 | * | (Incorrect. The amounts of pounds for the walnuts and cashews are interchanged. Which answer choice does not have them interchanged?)
A:  | Total cost ($) | = | Price ($/pound) | * | Amount (pounds)
Walnuts |  | = | 7.60 | * |
Cashews | 72.00 | = | 12.00 | * | 6
Total Mix |  | = | 9.25 | * |

Q: Eva created a coffee blend for her restaurant by mixing Kenya and French Roast coffee beans. The Kenya beans cost $15 per pound and the French Roast costs $8 per pound. She bought a total of 10 pounds of coffee for a total of $97.50.

How much of each type of bean did she buy?
- 3 lbs Kenya and 7 lbs French Roast (Incorrect. Use the following system to set up this problem: Where k represents the amount of Kenya coffee, and f represents the amount of French Roast coffee. Use substitution or elimination to solve for k and f.)
- 4 lbs Kenya and 6 lbs French Roast (Incorrect. Use the following system to set up this problem: Where k represents the amount of Kenya coffee, and f represents the amount of French Roast coffee. Use substitution or elimination to solve for k and f.)
- 1.5 lbs Kenya and 8.5 lbs French Roast (Incorrect. Use the following system to set up this problem: Where k represents the amount of Kenya coffee, and f represents the amount of French Roast coffee. Use substitution or elimination to solve for k and f.)
- 2.5 lbs Kenya and 7.5 lbs French Roast (Correct. 2.5 lbs Kenya and 7.5 lbs French Roast is 10 lbs of coffee, for a total of $97.50.)
A: 2.5 lbs Kenya and 7.5 lbs French Roast

Q: A chemist needs 40 liters of 20% acid solution. She has containers of 10% solution and 40% solution.

How many liters of each should she combine to get the needed solution?
- 26 liters of the 10% solution, and 14 liters of the 40% solution (Incorrect. Filling in the chart will help obtain the equation you need to find the answer: | Acidity | | Amount of sol. (liters) | | Amount of acid (liters) Sol. 1 | 10% | * | | = | Sol. 2 | 40% | * | | = | Mix | 20% | * | 40 | = | 8 This gives you an equation of: . When you solve for x, look back to the chart to see that x represents the amount of liters of solution 1 you will need. Subtract to find the amount of liters of solution 2 you will need.)
- liters of the 10% solution, and liters of the 40% solution (Correct. liters of the 10% solution and liters of the 40% solution will give you the acid solution needed.)
- 12 liters of the 10% solution, and 28 liters of the 40% solution (Incorrect. Filling in the chart will help obtain the equation you need to find the answer: | Acidity | | Amount of sol. (liters) | | Amount of acid (liters) Sol. 1 | 10% | * | | = | Sol. 2 | 40% | * | | = | Mix | 20% | * | 40 | = | 8 This gives you an equation of: . When you solve for x, look back to the chart to see that x represents the amount of liters of solution 1 you will need. Subtract to find the amount of liters of solution 2 you will need.)
- 20 liters of the 10% solution, and 20 liters of the 40% solution (Incorrect. Filling in the chart will help obtain the equation you need to find the answer: | Acidity | | Amount of sol. (liters) | | Amount of acid (liters) Sol. 1 | 10% | * | | = | Sol. 2 | 40% | * | | = | Mix | 20% | * | 40 | = | 8 This gives you an equation of: . When you solve for x, look back to the chart to see that x represents the amount of liters of solution 1 you will need. Subtract to find the amount of liters of solution 2 you will need.)
A: liters of the 10% solution, and liters of the 40% solution

Q: Consider the system of inequalities:

Which of the following graphs correctly represents this system?
A: (a choice with no text)
If wrong: Incorrect. The inequality is a solid line with shading below it, and the inequality is a dotted line with shading above it. Go back and check that the lines drawn are correctly dotted or solid in accordance with their inequality sign.
If right: Correct. The inequality is a solid line with shading below it, and the inequality is a dotted line with shading above it.
If wrong: Incorrect. The inequality is a solid line with shading below it, and the inequality is a dotted line with shading above it. Go back and check that the lines drawn are correctly dotted or solid in accordance with their inequality sign.
If wrong: Incorrect. The inequality is a solid line with shading below it, and the inequality is a dotted line with shading above it. Go back and check that the lines drawn are correctly dotted or solid in accordance with their inequality sign.

Q: Consider the system of inequalities:

Which of the following bounded regions correctly represents the solution of this system of inequalities?
A: (a choice with no text)
If wrong: Incorrect. Make sure you have correctly graphed both inequalities. Double-check your shading to make sure you are shading in the right direction.
If wrong: Incorrect. Make sure you have correctly graphed both inequalities. Double-check your shading to make sure you are shading in the right direction.
If right: Correct. Graphing and shading both inequalities gives you the graph of:
If wrong: Incorrect. Make sure you have correctly graphed both inequalities. Double-check your shading to make sure you are shading in the right direction.

Q: Consider the system of inequalities:

After graphing and shading the inequalities, which region in the grid below would represent the solution region?
- Region A (Incorrect. If you're having trouble graphing, try picking a point in Region A, and plugging in its coordinates for x and y in the inequalities. If the inequalities are both true with those values, then that is the correct region. If not, move onto other regions and other points.)
- Region B (Incorrect. If you're having trouble graphing, try picking a point in Region A, and plugging in its coordinates for x and y in the inequalities. If the inequalities are both true with those values, then that is the correct region. If not, move onto other regions and other points.)
- Region D (Correct. Graphing and shading both inequalities gives you the graph of: Since the green region is the solution to the system, Region D is the correct answer.)
- Region C (Incorrect. If you're having trouble graphing, try picking a point in Region A, and plugging in its coordinates for x and y in the inequalities. If the inequalities are both true with those values, then that is the correct region. If not, move onto other regions and other points.)
A: Region D

Q: Consider the system of inequalities:

Which one of the following coordinates is a solution to the system?
- (-4, -4) (Incorrect. The only way that a point can be a solution to the system is if both statements are true when the point is plugged into them. Check that your initial solution works for both inequalities.)
- (0, 0) (Incorrect. The only way that a point can be a solution to the system is if both statements are true when the point is plugged into them. Check that your initial solution works for both inequalities.)
- (6, 6) (Incorrect. The only way that a point can be a solution to the system is if both statements are true when the point is plugged into them. Check that your initial solution works for both inequalities.)
- (-7, 3) (Correct. Plugging in (-7, 3) to yields two true statements: All other points yield at least one false statement, so (-7, 3) is the solution.)
A: (-7, 3)

Q: Consider the system of inequalities and its non-shaded graph:

After graphing and shading the inequalities, which region in the grid below would represent the solution region?
- Point C (Incorrect. Determine the exact coordinates for all four points (and keep in mind that the grid lines are every two units!). When you plug each point into the system, which point makes both inequalities true?)
- Point A (Incorrect. Determine the exact coordinates for all four points (and keep in mind that the grid lines are every two units!). When you plug each point into the system, which point makes both inequalities true?)
- Point B (Correct. Point B (2, 6) is the solution because when plugged into both inequalities, they result in true statements:)
- Point D (Incorrect. Determine the exact coordinates for all four points (and keep in mind that the grid lines are every two units!). When you plug each point into the system, which point makes both inequalities true?)
A: Point B