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Grade 7–9Common Core (CCSS) · Math: algebra

Systems of Equations — Worksheets with Answers

Practise solving two equations with two unknowns, with whole-number solutions every time.

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Systems of equations · 14-16 years

Name: ____________________

Worked example

  1. The goal: find the values of x and y that make both equations true at the same time.
  2. Two equations, two unknowns. Example: x + y = 10 and x − y = 2.
  3. Add the equations: (x + y) + (x − y) = 10 + 2 → 2x = 12 → x = 6.
  4. Put x into the first: 6 + y = 10 → y = 4. Answer: x = 6, y = 4.
  5. Check: read the question again. Does your answer give what was asked, with the right unit? Work backwards to see that it fits. ✓
Example: how to solve it
1.

Solve the system: −3x + y = 0 and 2x + 3y = 0

2.

Solve the system: −2x + y = 3 and −3x + 3y = 0

3.

Solve the system: x + y = 2 and x − y = −2

4.

Solve the system: −x − y = −1 and −3x + y = −23

5.

Solve the system: 2x − y = 5 and −3x + 2y = −9

6.

Solve the system: −2x − y = −23 and −2x + 2y = −2

7.

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

8.

Solve the system: −3x + 3y = 21 and 4x − y = −13

9.

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

10.

Solve the system: −2x + 2y = 10 and 3x − y = −1

11.

Solve the system: −x − 2y = 15 and 3x − 2y = −5

12.

Solve the system: −x + 3y = 0 and −3x + 3y = 0

13.

Solve the system: −2x − 3y = −8 and 2x + y = 12

14.

Solve the system: x − 3y = −17 and 2x + 3y = 38

15.

Solve the system: 4x + 3y = 41 and −2x + y = −13

16.

Solve the system: x + y = −2 and 2x − y = 2

17.

Solve the system: x − 3y = 7 and x + 2y = −8

18.

Solve the system: −3x − 2y = −14 and 2x − 2y = 26

19.

Solve the system: x + 3y = 16 and −2x − y = 3

20.

Solve the system: −3x + y = −17 and 3x + 2y = 11

Answer key

  1. 1. x = 0, y = 0
  2. 2. x = −3, y = −3
  3. 3. x = 0, y = 2
  4. 4. x = 6, y = −5
  5. 5. x = 1, y = −3
  6. 6. x = 8, y = 7
  7. 7. x = 0, y = 3
  8. 8. x = −2, y = 5
  9. 9. x = 0, y = 2
  10. 10. x = 2, y = 7
  11. 11. x = −5, y = −5
  12. 12. x = 0, y = 0
  13. 13. x = 7, y = −2
  14. 14. x = 7, y = 8
  15. 15. x = 8, y = 3
  16. 16. x = 0, y = −2
  17. 17. x = −2, y = −3
  18. 18. x = 8, y = −5
  19. 19. x = −5, y = 7
  20. 20. x = 5, y = −2

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Topics on this worksheet

Areas on this sheet

  • Algebra · 20

Step 1 of 5

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Area
Algebra
Exercise type
Systems of equations
Age
14–16 years
Difficulty
Easy
Number of tasks
20
Task format
Calculations
Paper size
US Letter
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Area
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How to use the tool

  1. Choose the exercise type systems of equations.
  2. Pick age group 12–14 or 14–16, difficulty and calculations, word problems or a mix.
  3. Print or save as PDF. “Create new version” gives new numbers with a matching answer key.

About this generator

A system of equations asks for the x and y that make two equations true at the same time. The easier level uses x + y and x − y so elimination is quick. Harder levels use other coefficients that call for substitution or multiplying an equation first. All solutions are whole numbers so pupils can check their work. The answer key is calculated by the website, so it always matches the tasks. No sign-up is needed and no personal data is collected.

Popular uses

  • Substitution and elimination
  • Grade 9 algebra
  • Revision before exams
  • Homework with answer key

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Frequently asked questions

How do I pick the right level?
Choose an age or grade in step 2. Start easier if the pupil is unsure – you can switch anytime and get new problems instantly.
Can I see the problems before printing?
Yes. The sheet shows exactly the problems that will print. Click New problems to swap them.
How do I include an answer key?
Turn on Answer key in the last step. It prints on its own page after the problems, with the same numbering.
What does the question mark next to a problem do?
It opens a step-by-step explanation of the method on screen. It is not printed and does not reveal the answer.
What is the elimination method?
Add or subtract the equations so one unknown disappears, then solve for the other.
How do I check my answer?
Put x and y into both equations; both must be true.

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