System of Equations Solver
Type two or three linear equations. You get the values that satisfy all of them at once, found with Cramer's rule.
Example — x + y = 5 and x − y = 1x = 3, y = 2
How we got it — the example, step by step
- The coefficient matrix has determinant D = (1)(−1) − (1)(1) = −2 — not zero, so exactly one solution exists.
- Cramer's rule for x: replace the x column with the right-hand sides → determinant −6, so x = −6 ÷ −2 = 3.
- Same for y: determinant −4, so y = −4 ÷ −2 = 2.
Check it backwards
Equation 1: left side = 5, right side = 5. Equation 2: left side = 1, right side = 1 — balanced.
Questions people also ask
What if there is no solution?
If the determinant is 0, the equations contradict each other or repeat each other, and the solver says there is no unique solution instead of inventing one.