System of Equations Solver

Solves systems of 2 to 4 linear equations, gives the solution as exact fractions and decimals, and writes out the elimination or substitution steps. Use it to check homework or to find the values of x and y quickly.

How to use

1. Under "Input", choose "Type equations" and write one equation per line, such as 2x + 3y = 7. To use a table instead, choose "Coefficient grid" and set "Unknowns".
2. The answer appears under "Solution". If there is no solution or infinitely many, the reason is shown.
3. Read the "Steps". With 2 equations in 2 unknowns, you can choose "Elimination" or "Substitution".
4. "Check" substitutes the solution into the original equations. With 2 unknowns, the "Graph" shows where the lines cross.

How it works

• All arithmetic uses exact fractions without rounding, so a solution such as 1/3 is shown exactly.
• Any letters can be unknowns, not only x, y and z, for example a, b or x1. Up to 6 equations and 4 unknowns are accepted.
• Equations with terms such as x² or xy are not linear and are not solved.
• Your equations are saved in this browser on this device.

Questions and answers

How does the elimination method work?

Make the coefficients of one unknown equal, then subtract or add the equations to remove it. For 2x + 3y = 7 and 3x + 2y = 8, multiply by 3 and by 2 and subtract: 5y = 5, so y = 1 and x = 2.

How does the substitution method work?

Solve one equation for one unknown and put the result into the other. Rewriting x + y = 5 as y = 5 − x and putting it into the other equation leaves one equation in x.

Can it solve 3 equations with 3 unknowns?

Yes. Enter three equations; the steps show how each unknown is removed and the values substituted back. Up to 4 unknowns are supported.

When does a system have no solution or infinitely many?

If elimination gives a false statement such as 0 = 3, there is no solution. If it gives 0 = 0 and too few equations remain, there are infinitely many. With 2 unknowns, these are parallel lines and identical lines.