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:

What you can do with the System of Equations

Substitution, elimination and matrix methods.

Enter your values or describe the problem in the calculator above. Review the result and the explanation before using it in homework, study or practical calculations.

Example input

e.g. solve x + y = 7 and 2x - y = 5

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).

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