8th Grade U4 pt 2 Test Corrections

1) Mateo plans to solve the system of equations by using elimination. What would be a reasonable first step he could take? 

-x + 6y = 9

3x + 2y = 13

• multiply the second equation by -3

• multiply the first equation by 2

• multiply the second equation by 2

• do not multiply, just use elimination

2) Solve the system of equations using elimination. YOU MUST SHOW WORK. Desmos should only be used to check your solution. 

-3x + 2y = 48

3x + y = 42

3) Solve the system of equations using elimination. YOU MUST SHOW WORK. Desmos should only be used to check your solution. 

3x + 2y = -17

x + y = -7

Which TWO qualities mean a graph has NO SOLUTION? (PICK TWO!)

• parallel lines

• same slope, different y-intercepts

• same line

• same slope, same y-intercept

Which TWO qualities mean a graph has INFINITELY MANY SOLUTIONS? (PICK TWO!)

• parallel lines

• same slope, different y-intercepts

• same line

• same slope, same y-intercept

Which TWO qualities mean a graph has ONE SOLUTION? (PICK TWO!)

• parallel lines

• different slopes

• intersecting lines

• same slope, same y-intercept

5) Jane is observing the system of equations below and thinks it will have exactly one solution. Is she correct? Why or why not? 

• No; the slopes are the same, but the y-intercepts are different, so there would be no solution to the system of equations.

• No; the slopes are the same and the y-intercepts are different, so there are infinite solutions.

• Yes; the slopes are the same, so they will intersect and have one solution.

• Yes; the y-intercepts are different, so they will intersect and have one solution.

6) At a movie theater, 2 medium drinks and a large popcorn costs $13.85. At the same theater, a family bought 3 medium drinks and 2 large popcorns for a total of $23.90. Which system of equations could be used to find x, the cost of a medium drink and y, the cost of a large popcorn?

• 
• 
• 
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7) Christine’s rectangular bedroom has a perimeter of 44 feet. The length of her bedroom is 2 feet more than the width. Which of the following is a true statement?

• The width of Christine’s bedroom is 10 feet.

• The length of Christine’s bedroom is 8 feet.

• Both A and B are true.

• Neither A nor B is true.