About solving linear systems
This solver finds the values of the unknowns in a system of linear equations — two or three variables. Enter the coefficients of each equation and it solves for x, y (and z) using Cramer's rule, telling you when there is no unique solution. It is perfect for algebra homework and quick checks, and runs in your browser.
How Linear Equations works
How to solve a system
- Pick 2 or 3 variables.
- Enter the coefficients and the right-hand value of each equation.
- Tap Solve to get x, y (and z).
Cramer's rule
The solver computes the determinant of the coefficient matrix and, for each variable, the determinant of that matrix with one column replaced by the answers. Dividing gives each variable. If the main determinant is zero, there is no unique solution.
No unique solution
A zero determinant means the equations are either inconsistent (no solution) or dependent (infinitely many) — the tool flags this so you do not get a misleading answer.
Common uses
- Solve 2 or 3 simultaneous equations
- Find x, y and z
- Check algebra homework
- Solve systems for science problems
- Verify hand-worked solutions
- Learn how Cramer’s rule works
- Solve engineering equations
- Quickly test a set of equations
Frequently asked questions
How do I solve simultaneous equations?
Enter each equation’s coefficients and result, then tap Solve to get the values of the unknowns.
How many variables are supported?
Two or three (2×2 or 3×3 systems).
What method does it use?
Cramer’s rule, based on determinants.
What if there is no unique solution?
If the determinant is zero, the tool tells you the system has no unique solution.
Can coefficients be negative or decimal?
Yes — enter any real numbers.
Is my data uploaded?
No — it solves entirely in your browser.
Does it show z for 2 variables?
No — only the variables you select are solved.
Is it free?
Yes — completely free with no sign-up.