System of Equations Calculator
Solve a system of two linear equations with two unknowns (x and y) using Cramer's rule.
- Free to use
- Accurate results
- No registration required
- Works on all devices
Enter the coefficients of two linear equations to solve for x and y.
Your result
3.2
x
y2.2
AI explanation
Formula
For a1x + b1y = c1 and a2x + b2y = c2, solved via Cramer's rule using the coefficient determinantWorked example
2x + 3y = 13, x − y = 1
| Field | Value |
|---|---|
| Equation 1 — coefficient of x | 2 |
| Equation 1 — coefficient of y | 3 |
| Equation 1 — constant | 13 |
| Equation 2 — coefficient of x | 1 |
| Equation 2 — coefficient of y | -1 |
| Equation 2 — constant | 1 |
| x | 3.2 |
| y | 2.2 |
Assumptions
- Supports exactly 2 equations with 2 unknowns — for a larger system, use the Matrix Calculator's row-reduction tools instead.
- If the two equations are parallel or identical (no unique solution), an error is shown instead of a result.
Frequently asked questions
What is Cramer's rule?
A method for solving a linear system using determinants — each variable's value is a ratio of two determinants formed from the system's coefficients.
What if the system has no unique solution?
This happens when the two equations are parallel (no solution) or identical (infinitely many solutions) — the calculator shows an error in that case.
Can this solve 3 equations with 3 unknowns?
Not this page — it's scoped to 2×2 systems. Use the Matrix Calculator for larger systems via matrix methods.