GACE Middle Grades Math: Systems of Linear Equations Chapter Exam

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Question 11.How many more equations are needed to complete this linear system with three variables?

Question 22.What are the most common letters we will see for our variables?

Question 33.

Solve this system.

4x + y = 12

x + y = 6

Question 44.Which graph does NOT represent a system of equations?

Question 55.

Which equation represents a valid first step to solving the following system of equations using the elimination method if our next step is to add the equations together to eliminate the x variable?

2x - 2y = 5 and -4x + 5y = 11

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Question 66.Solve this system.

Question 77.What is the first step in the substitution method?

Question 88.If two equations produce a false statement in a linear system in three variables, how many solutions does this system have?

Question 99.If a linear system has three variables, how many equations are needed to complete the system?

Question 1010.How many solutions does this system have?

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Question 1111.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 1212.

Solve the following system of equations:

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

Question 1313.Consider the following two car rental companies. Cars R Us charges $100 up front, plus 10 cents per mile. Thrifty Car Rentals charges 25 cents per mile with no upfront fee. If TC represent the total cost for the car, and n represents the number of miles, which of the following systems of equations best represents this situation?

Question 1414.Based on this graph, what is the solution to the system of equations?

Question 1515.

Which of the following represents a valid first step to solving this system of equations using the substitution method?

2x - y = 7

x = 2y - 1

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Question 1616.When trying to figure out how many $5 burritos and $3 tacos to buy, which equation represents the situation where you have $100 to spend?

Question 1717.Which method can be used to solve any system of linear equations in two variables?

Question 1818.Which of the following will work?

Question 1919.How many solutions does this system have?

Question 2020.Which of the following is a solution to the system of equations shown in the graph below?

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Question 2121.

Solve the system of equations below:

y = 3x - 5

y = -2x + 10

Question 2222.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 2323.

Solve.

x - y = 6

x + y = 10

Question 2424.How many variables does a linear system in three variables have?

Question 2525.

Solve this system.

x + y = 6

y = 2x

GACE Middle Grades Math: 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
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to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will
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Click it to see your results. Good luck!