Systems of Equations Worksheet with Answers – Grade 8 (Free PDF)

Problem 1 Is it a solution? ★★★

Decide whether each ordered pair is a solution of the system.

x + y = 5
2x − y = 4

(a) (3, 2) (b) (4, 1)

Problem 2 Read the intersection ★★★

Use the graph to find the solution of the system y = 2x − 1 and y = −x + 5.

Problem 3 Substitution, warm-up ★★★

Solve by substitution:

y = 2x
x + y = 12

Problem 4 Elimination, warm-up ★★★

Solve by elimination:

x + y = 9
x − y = 3

Problem 5 Equal expressions ★★★

Solve the system y = x + 6 and y = 4x − 3.

Problem 6 Estimate and verify ★★★

The lines y = x − 2 and y = −2x + 7 are graphed. Estimate the solution and verify it in both equations.

Problem 7 Substitute an expression ★★★

Solve by substitution:

x + 2y = 11
x = 3y − 4

Problem 8 Add to eliminate ★★★

Solve by elimination:

3x + 2y = 16
x − 2y = 0

Problem 9 Multiply, then eliminate ★★★

Solve by elimination:

2x + 3y = 13
4x − y = 5

Problem 10 Scale one equation ★★★

Solve by elimination:

x + 4y = 21
3x + 2y = 13

Problem 11 Parallel lines ★★★

Look at the graph of 2x + 3y = 6 and 2x + 3y = 12. How many solutions does the system have? Explain by comparing slopes.

Problem 12 Same line ★★★

Determine how many ordered pairs satisfy both equations of this system, and justify your answer.

y = 5x − 4
10x − 2y = 8

Problem 13 Classify without solving ★★★

Without solving, say whether each system has one solution, none or infinitely many: (a) y = 3x + 1 and y = 3x − 4 (b) y = −x + 2 and y = 2x + 2 (c) 2x + y = 4 and 4x + 2y = 8

Problem 14 Two lines, one point ★★★

Solve the system y = −2x + 9 and y = 3x − 6.

Problem 15 Bake sale ★★★

At a school bake sale, muffins cost $2 and brownies cost $3.50. Students sold 40 items for $95 in total. How many muffins (x) and how many brownies (y) were sold?

Problem 16 Trail meet-up ★★★

Ana starts 2 miles up a trail and walks away at 3 miles per hour. Ben starts at the trailhead and walks the same way at 4 miles per hour. The graph shows both, with hours on the x-axis and miles on the y-axis. Write a system, find when Ben catches Ana, and how far they are from the trailhead.

Problem 17 Concert tickets ★★★

Adult tickets cost $12 and child tickets cost $7. A total of 150 tickets were sold for $1,330. How many of each were sold?

Problem 18 Rectangle dimensions ★★★

A rectangle has a perimeter of 56 feet. Its length is 1 foot more than twice its width. Find the length and width.

Problem 19 Build a system ★★★

Write a system of two linear equations whose only solution is (4, −1). Verify your system.

Problem 20 Car rental ★★★

Company A charges $35 per day plus $0.20 per mile. Company B charges $20 per day plus $0.35 per mile. At how many miles do the daily costs match? Which company is cheaper for 250 miles?