# Solving Systems of Linear Equations Chapter Exam

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#### Question 1 1. Craig is new at Bleachy Clean Cleaning Services. He needs to make 12 gallons of cleaner with a 15% concentration of bleach. He only has cleaners with 10% and 30% solutions. How many gallons of the 10% solution will he need?

#### Question 2 2. Which of the following will work?

####
Question 3
3.
Solve.

x - y = 6

x + y = 10

#### Question 4 4. Look at the graph. What is the solution to the system of equations?

#### Question 5 5. How many more equations are needed to complete this linear system with three variables?

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#### Question 6 6. At the end of his weekly shopping excursion, Mr. Archer has purchased six pairs of pants and five pairs of socks for $348. The next day, he realizes he needs one more pair of pants and two pairs of socks, which he buys for $72. If the prices for all the pants are equal, as are the prices for all the socks, what is the cost of one pair of socks?

#### Question 7 7. If 6x - 3y = -12 and 2x + 2y = -10, then y =

#### Question 8 8. If x + y = 6 and 3x + 2y = 4, then y =

#### Question 9 9. A car company has $44,000 to spend on robots to put paint on new cars. There are 2 types of robots, some that cost $3,000 and some that cost $2,000. If the company is sure that it wants to spend all of its money on 16 new robots, how many of each should it purchase?

#### Question 10 10. If trying to figure out how many $5 burritos and $3 tacos to buy, which equation represents the situation where you have $100 to spend?

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####
Question 11
11.
Which equation represents the first step to solving the following system of equations using the substitution method?

2x - y = 7

x = 2y - 1

#### Question 12 12. If 5x + 2y = 9 and -3x + 6y = 9, then y =

#### Question 13 13. How many solutions does this system have?

#### Question 14 14. Solve this system.

#### Question 15 15. What are the most common letters we will see for our variables?

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#### Question 16 16. The Rusty Metal Roller Coaster at the fair charges $2.50 for children and $4 for adults. Before the safety inspector shuts down the ride, 260 people ride it and $815 is collected. How many adults rode the coaster?

#### Question 17 17. Today, Archie is 27 years older than his son, Peyton. In 4 years, Archie will be 3 years shy of 4 times Peyton's age. How old is Archie today?

#### Question 18 18. What is the solution to the system of equations shown in the graph below?

####
Question 19
19.
Solve this system.

4x + y = 12

x + y = 6

#### Question 20 20. If 4x - 7y = 14 and 2x - 4y = 6, then y =

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####
Question 21
21.
Solve this system.

x + y = 6

y = 2x

#### Question 22 22. If x - y = 7 and 2x + 5y = 0, then y =

####
Question 23
23.
Find the solution, given the system of equations below.

y = 3x - 5

y = -2x + 10

#### Question 24 24. If you don't see a variable listed in a linear system in three variables, you should note that the variable has a coefficient of:

#### Question 25 25. How many solutions does this system have?

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#### Question 26 26. How many variables does a linear system in three variables have?

#### Question 27 27. If a linear system has three variables, how many equations are needed to complete the system?

####
Question 28
28.
Solve the following system of equations:

2x - 3y = 21 and 5x + 4y = 18

#### Question 29 29. Two companies charge different amounts for renting a car. Company A charges a lot up front, but not much per day. Company B lets you have the car for cheap, but then makes you pay a lot every day you have the car. If we have two equations that represent these two companies, and we solve this system of equations, what will we find?

#### Question 30 30. Which graph does NOT represent a system of equations?

#### Solving Systems of Linear Equations Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!