System of Equations Solver

Solve systems of two or three linear equations. Get step-by-step solutions using substitution, elimination, or matrix methods.

A system of equations involves two or more equations with the same variables. Solving them means finding the values that satisfy all equations simultaneously. Our solver handles systems of two or three equations and shows you the solution using elimination, substitution, or matrix methods, whichever is most efficient for the given problem.

How It Works

Enter your equation or expression into the solver above and click "Solve." Our system first attempts a deterministic verification using a symbolic math engine for guaranteed accuracy. If verified, you will see a Verified badge next to the answer.

Example Problem

2x + y = 7 and x - y = 2

Step-by-Step Solution

  1. Write the system: 2x + y = 7 ... x - y = 2
  2. Add both equations to eliminate y: 3x = 9
  3. Solve for x: x = 3
  4. Substitute x = 3 into x - y = 2: 3 - y = 2, so y = 1
Final Answer: x = 3, y = 1

Frequently Asked Questions

What is a system of equations?
A system of equations is a set of two or more equations that share the same variables. The solution is the set of values that makes all equations true at the same time.
What methods can solve a system of equations?
Common methods include substitution, elimination (adding/subtracting equations), graphing, and matrix methods such as row reduction or Cramer's rule.
Can a system of equations have no solution?
Yes. If the equations represent parallel lines (same slope, different intercepts), there is no solution. If they represent the same line, there are infinitely many solutions.

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