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Grade 8 Systems of linear equations Worksheets

Grade 8 practice: Find the ordered pair that satisfies two linear equations. Choose a level below to generate a fresh set of questions.

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Understanding systems of linear equations

A system of linear equations is two equations that must both be true at once. The solution is the ordered pair of values that satisfies both, which graphically is the point where the two lines cross. Students can solve by substitution or elimination, or verify a given pair by checking it in both equations. This underlies much of later algebra.

For x + y = 10 and x − y = 2, adding the equations eliminates y: 2x = 12, so x = 6, and then y = 4. The pair (6, 4) satisfies both equations. A common mistake is finding a pair that fits one equation but not the other and stopping there. Tip: once you have a candidate pair, substitute it into both original equations; it is only the solution if both statements come out true.

Sample systems of linear equations questions

These examples come from the Easy setting. Generate a worksheet for a complete page with space for working.

Solve: 1x + 5y = 23; 1x − 4y = -13.
Solve: 2x + 3y = -3; 1x − 5y = 31.
Solve: 1x + 2y = -6; 1x − 2y = 2.
Solve: 1x + 5y = 4; 5x − 3y = -8.

Check the sample answers

(3, 4)
(6, -5)
(-2, -2)
(-1, 1)

Practice focus

Find the ordered pair that satisfies two linear equations. Show each step and check the answer.

Grade 8 Systems of linear equations Worksheets

Understanding systems of linear equations

Sample systems of linear equations questions

Practice focus

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