System of Equations

Solve two or three simultaneous equations by substitution, elimination or matrices, with each move explained. Try “solve x + y = 7 and 2x − y = 5”.

Try an example:

How the System of Equations works

  1. Pick a method: substitution if a variable is easy to isolate, elimination if coefficients line up.
  2. Eliminate or substitute to reduce to one equation in one variable and solve it.
  3. Back-substitute to find the other variable and check in both original equations.

Frequently asked questions

What is the difference between substitution and elimination?

Substitution replaces one variable with an expression from another equation. Elimination adds or subtracts equations to cancel a variable.

Can a system have no solution?

Yes. Parallel lines never meet (no solution), and identical lines meet everywhere (infinitely many solutions).

More Algebra calculators

Linear Equation SolverSolve one-variable equations with balancing steps. Quadratic Equation SolverFactoring, completing the square and the quadratic formula. Inequality SolverLinear, quadratic and absolute-value inequalities with number lines. Factoring & ExpandingFactor or expand polynomials and expressions. Polynomial DivisionLong division and synthetic division, remainder theorem. Exponential & Log EquationsSolve equations with powers and logarithms.

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