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Systems of equations worksheet

Grade 8 math, Common Core 8.EE.C.8. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

By the StudyWiz teamUpdated October 23, 2026How we write our pages

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Systems of equations

Grade 8 math, Common Core 8.EE.C.8

Solve each system. Write the solution as an ordered pair (x, y).

  1. 1.
    y = 4x + 30 and y = −2x − 6
  2. 2.
    y = −3x + 4 and y = 3x + 10
  3. 3.
    How many solutions does this system have? y = x − 5 and 2y = 2x − 10
  4. 4.
    3x + 3y = 12 and 4x − 2y = −32
  5. 5.
    x − 3y = 18 and 2x − y = 11
  6. 6.
    y = 3x − 23 and y = 2x − 16
  7. 7.
    How many solutions does this system have? y = −3x + 1 and 2y = −6x + 2
  8. 8.
    Adult tickets cost $13 and child tickets cost $4. A group bought 35 tickets for $347. How many of each did they buy?
  9. 9.
    Adult tickets cost $6 and child tickets cost $4. A group bought 44 tickets for $216. How many of each did they buy?
  10. 10.
    How many solutions does this system have? y = −2x + 4 and y = −2x + 1
Free worksheets for grades 6 to 8 from StudyWiz, with answer keys: studywiz.online/worksheets

Answer key: Systems of equations

Grade 8 math. Each answer has a few worked steps, to help check the method as well as the answer.

  1. 1. (−6, 6)

    4x + 30 = −2x − 66x = −36x = −6, then y = 6

  2. 2. (−1, 7)

    −3x + 4 = 3x + 10−6x = 6x = −1, then y = 7

  3. 3. Infinitely many: it is the same line.

  4. 4. (−4, 8)

    Check: 3(−4) + 3(8) = 12and 4(−4) − 2(8) = −32

  5. 5. (3, −5)

    Check: 3 − 3(−5) = 18and 2(3) − (−5) = 11

  6. 6. (7, −2)

    3x − 23 = 2x − 16x = 7x = 7, then y = −2

  7. 7. Infinitely many: it is the same line.

  8. 8. 23 adult and 12 child tickets

    a + c = 3513a + 4c = 347

  9. 9. 20 adult and 24 child tickets

    a + c = 446a + 4c = 216

  10. 10. No solution: the lines are parallel.

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About systems of equations

A system of equations is two equations that are true at the same time. Its solution is the point (x, y) where their graphs cross. Solve by substitution (put one equation into the other) or elimination (add or subtract the equations to cancel a variable). Parallel lines never cross, so their system has no solution.

Worked example 1

Adult tickets cost $10 and child tickets cost $4. A group bought 25 tickets for $118. How many of each did they buy?
  1. Step 1.a + c = 25
  2. Step 2.10a + 4c = 118

Answer: 3 adult and 22 child tickets

Worked example 2

y = x and y = −3x + 24
  1. Step 1.x = −3x + 24
  2. Step 2.4x = 24
  3. Step 3.x = 6, then y = 6

Answer: (6, 6)

Worked example 3

x + y = 4 and x − y = 6
  1. Step 1.Add the equations: 2x = 10, so x = 5
  2. Step 2.5 + y = 4, so y = −1

Answer: (5, −1)

Watch out for

  • If one equation already says y = …, substitute it into the other.
  • To eliminate, make the x (or y) numbers opposites, then add the equations.
  • Check your pair in both equations, not just one.

Practice systems of equations online

On StudyWiz, your kid can practice systems of equations with 5-question quizzes that are checked as they go, with an explanation for every answer. When a homework problem is the trouble, Wiz gives a hint for each step instead of the answer.

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