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System of Two Equations

Solve 3x + 2y = 12, 2x - y = 1

Answer

x = 2, y = 3

Working

  1. Put both equations in standard form

    Rearrange to a·x + b·y = c. That gives 3x + 2y = 12 and 2x - y = 1.

  2. Compute the determinant

    The coefficient determinant is D = (3)(-1) − (2)(2) = -7. Since D ≠ 0 the system has a unique solution.

  3. Apply Cramer's rule

    Replace the x column with the constants and take Dx = (12)(-1) − (1)(2) = -14. Then x = Dx / D = 2.

  4. Solve for y

    Likewise Dy = (3)(1) − (2)(12) = -21, so y = Dy / D = 3.

Equations

Intermediate equations in the working
ExpressionResult
D = a1·b2 − a2·b1-7
x = Dx / D2
y = Dy / D3
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