LEAP 2025 Math Grade 8 Chapter 7

**Answer questions 1–3 about the description below.**

Lucas is choosing between carpet cleaners for his home. Ability Best charges a $40 flat rate and then $2 per 100 square feet of carpet. Carpet Pro charges a $25 flat rate and then $3.50 per 100 square feet of carpet.

1 pt

2.

At what point do the two carpet cleaners charge the same amount for their services?

1 pt

5.

Select a graph of a system of two equations that has a single solution of (5, –3)

A

B

C

D

1 pt

10.

Which statement about this linear system must be true?

$2x=4y-1\phantom{\rule{0ex}{0ex}}y=\frac{1}{2}x+\frac{1}{4}$

A

x = 0

B

y = 0

C

There is no solution to this system.

D

There are infinitely many solutions to this system.

1 pt

12.

Two lines are shown on the grid. One line passes through the origin, and the other passes through (−1, −1) with a y-intercept of 2. Which pair of equations below the graph identifies these lines?

A

$y=\frac{1}{4}x,andy=\frac{1}{3}x+2$

B

$x-2y=6,and4x+y=4$

C

$y=4x,andy=\frac{1}{3}x$

D

$y=3x+2,andy=-4x$