Simultaneous Equations Solver
Solve a system of two linear equations with two unknowns using Cramer's rule. Enter coefficients for a1*x + b1*y = c1 and a2*x + b2*y = c2.
X Val
1.000000
Det-14.0000
How to Solve Simultaneous Equations
Cramer's Rule for 2×2 Systems
Given:
Determinant D = a₁b₂ - a₂b₁
x = (c₁b₂ - c₂b₁) / D
y = (a₁c₂ - a₂c₁) / D
If D = 0, the system has no unique solution (the lines are parallel or identical).
Example Calculation
Solve: 2x + 3y = 8 and 4x - y = 2.
- 01D = (2)(-1) - (4)(3) = -2 - 12 = -14
- 02x = (8×(-1) - 2×3) / (-14) = (-8 - 6) / (-14) = -14 / -14 = 1
- 03y = (2×2 - 4×8) / (-14) = (4 - 32) / (-14) = -28 / -14 = 2
- 04Solution: x = 1, y = 2
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