System of Equations Calculator
Solve two equations in x and y, or three equations in x, y and z.
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Solution
- System
- Determinants
- Check
- Work
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Solving Systems with Cramer’s Rule
For ax + by = e, cx + dy = f: D = ad − bc, x = (ed − bf) ÷ D, y = (af − ce) ÷ D
For three equations, each variable equals the determinant with that variable’s column replaced by the constants, divided by the main determinant D. If D = 0 there’s no single solution.
Worked Example
Tips
Substitution and elimination give the same answer. The check line plugs the solution back into each equation.