Chamblee Middle School

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Coordinate Algebra EOC (GSE) Quiz Answer Key

Reasoning with equations and inequalities - (MGSE9-12.A.REI.5 ) System Of Equations

Student Name: _______________________

Teacher Name: THUYNGA DAO

1)

Solve the system of equations. A) x = 1, y = 2 B) x = 2, y = 1 C) x = 1, y = 1 D) x = 0, y = 2

x + 3y = 5 -x + 6y = 4

Explanation: The solution is x = 2, y = 1. You can solve the system by eliminating one of the variables.

x + 3y = 5 -x + 6y = 4 -----------9y = 9 y = 1

Then substitute 1 into one of the equations. x + 3(1) = 5 x = 2

2)

Solve the system of equations. A) x = 0, y = 3 B) x = 3, y = 0 C) x = 1, y = -2 D) x = -2, y = 1

2x - 2y = 6 3x + 2y = 9

Explanation: The solution is x = 3, y = 0. You can solve the system by eliminating one of the variables.

2x - 2y = 6 3x + 2y = 9 -----------5x = 15 x = 3

Then substitute 3 into one of the equations. 3(3) + 2y = 9 2y = 0 y = 0



Date: _________ Score: _________

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3)

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A system of linear equations has been graphed in the diagram. Determine a reasonable solution for the system of equations. A) (1, 1) B) (-2, 1) C) (-1, 1) D) (1, -1)

Explanation: The solution is (1, -1). Since the intersection point lies in quadrant IV, the coordinate of intersection must be (+, -).

4)

Use the graph method to solve the system of linear equations:

y - x = -2 and 2x + y = 7 A) (0,7) B) (2,0) C) (3.5,0) D) (3,1)

Explanation: (3,1) is correct. To graph the equations they need to be in slope-intercept form, or y = mx + b. By plotting the points we see that the system of equations intersect at (3,1). Thus, the solution is (3,1).

5) Solve the system of equations.

3x + y = 3 x + y = 2



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A)

B) C) D)

x = 1, y = 3 2

x = 3, y = 1 2

x = 1, y = 3 22

x = 3, y = 1 22

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Explanation: The solution is x = 1 , y = 3 . You can solve the system by subtracting the 2nd equation from the 1st.

22 3x + y = 3 x + y = 2 -----------2x = 1 x= 1

2 Then substitute 1 into one of the equations.

2 3( 1 ) + y = 3

2 y= 3

2



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6)

Solve the system of equations. A) x = 1 , y = 3 2 B) x = 3, y = 1 2 C) x = 4, y = - 3 2 D) x = - 3 , y = 4 2

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4x + 3y = 6 -4x + 2y = 14

Explanation: The solution is x = - 3 , y = 4. You can solve the system by adding the 2 equations together.

2 4x + 3y = 6 -4x + 2y = 14 -----------5y = 20 y = 4 Then substitute 4 into one of the equations. 4x + 3(4) = 6 4x = -6 x = -3

2

7)

Johanna has to solve the system of equations using substitution. She isolates x in the second equation. Which should be her next step?

A) 3(10 - 5y) + 6y =12 B) 30 - 15y + 6y = 12 C) 30 - 9y = 18 D) -9y = 18

Explanation: Now that she has isolated a variable she needs to substitute into the first equation to get them in terms of one variable. 3(10 - 5y) +



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6y =12 should be her next step as she is now substituting in to rewrite in terms of one variable.

8)

(1) Ax + By = C (2) Dx + Ey = F

Ralph is trying to solve the system of equations. He begins by subtracting Ax from both sides of equation (1), and then he divides the equation by B. Before he can continue, his friend Alice comes along and says, "No, you should have subtracted By from both sides, and then divided by A. You will get the wrong answer."

Is Alice right? Why or why not? A) Yes; Ralph's way will make y disappear, resulting in no solution. B) Yes; Ralph should isolate x in both equations. Now his answer will be wrong. C) No; Ralph is substituting for y, Alice is substituting for x. Both ways will work. D) No; Ralph is using substitution, while she is trying to use elimination. Both ways will work.

Explanation: No; Ralph is substituting for y, Alice is substituting for x. Both ways will work.



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9)

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(1) Ax + By = C (2) Dx + Ey = F

Jim is trying to solve the system of equations. He begins by multiplying equation (1) by D and equation (2) by A. Before he can continue, his friend Angela comes by and says, "No, you should have multiplied equation (1) by E and equation (2) by B. You're going to get the wrong answer."

Is Angela right? Why or why not? A) Yes; Jim's way will make both variables disappear, resulting in no solution. B) No; Jim is using elimination, Angela is using substitution. Both ways will work. C) No; Jim is trying to eliminate x, while she is trying to eliminate y. Both ways will work. D) Yes; Jim should have multiplied both equations by the same number. Now his answer will be wrong.

Explanation: No; Jim is trying to eliminate x, while she is trying to eliminate y. Both ways will work.

10)

A: 5x - 2y = 10 B: 4x + 3y = 7

To solve this system of equations by eliminations, what could you multiply each equation by to cancel out the y-variable? A) Multiply A by 3 and B by 2 B) Multiply A by 4 and B by 5 C) Multiply A by -3 and B by 2 D) Multiply A by 4 and B by -5

Explanation: Multiply A by 3 and B by 2 in order to cancel out the y-variable when adding the equations together.

The resulting equations would be: A: 15x - 6y = 30 B: 8x + 6y = 14

When combined, the y-variable cancels and you're left with 23x = 44

11)

How many solutions does the system have? A) 0 B) 1 C) 2 D) 3

Explanation: You can either graph the system and see two intersections or your can solve algebraically. To solve algebraically, substitute y = 4x + 1 into the quadratic equation y = x2 + 4 and solve: 4x + 1 = x2 + 4 0 = x2 - 4x + 3 0 = (x - 3)(x - 1) x = 3, x = 1 So the 2 solutions are (3, 13) and (1, 5).



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12)

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3x - 2y = 10 5x + y = 4

When solving this system of equations by elimination, which could be the resulting equation when a variable has been eliminated? A) 13x = 18 B) -7x = 2 C) -7y = 62 D) 8x - y = 14

Explanation: When you multiply the second equation by 2 and add it to the first equation the resulting equation is 13x = 18.

13) Which one is a solution to the system of equations?

x + 3y = 18 x + 2y = 14

A) (6, 4) B) (4, 6) C) (6, -4) D) (-4, 6)

Explanation: (6, 4)

x + 3y = 18 x + 2y = 14

First, solve either equation for either variable.

x + 3y = 18 x = 18 - 3y

Then substitute x into second equation, to solve for y.

18 - 3y + 2y = 14 18 - y = 14 -y = -4 y = 4

Then substitute y into second equation, to solve for x.

x = 18 - 3y x = 18 - 3(4) x = 18 - 12 x = 6



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