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Simultaneous Equations Calculator

Solve a pair of simultaneous equations by elimination, the way it is set out in class: label the equations, scale them so a variable matches, subtract, then substitute back. Every line of algebra is shown, so you can find the exact step where your own working went a different way.

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    Worked Example

    Solve 2x + 3y = 12 and x − y = 1.

    1. Multiply the second equation by 2 so the x terms match:2x − 2y = 2
    2. Subtract it from the first, and the x terms cancel:5y = 10
    3. Solve:y = 10 ÷ 5 = 2
    4. Substitute y = 2 into x − y = 1:x − 2 = 1, so x = 3

    Answer: x = 3, y = 2

    Try These Yourself

    Solve x + y = 10 and x − y = 4.Show answerHide answer

    Answer: x = 7, y = 3

    Add the equations: 2x = 14, so x = 7.

    Solve 3x + 2y = 16 and x + 2y = 8.Show answerHide answer

    Answer: x = 4, y = 2

    Subtract: 2x = 8, so x = 4, then 4 + 2y = 8.