Math · Linear systems

Understand simultaneous equations with elimination, substitution, and graph

Switch views to see how elimination and substitution work, with parentheses enforced for substitution and a graph to confirm the intersection. Fractions/decimals, vertical or horizontal lines, and no or infinite solutions are handled, and you can copy a share URL, LaTeX, SVG graph, or turn on teacher mode.

We auto-calculate the first sample on load. Input stays in your browser.

Languages: English | 日本語 | Español

× ÷ and full-width input are normalized automatically. Implicit multiplication like 2x or (x+1)(y-1) is supported.

How to use (3 steps)

  1. Enter two equations (× and full-width text are OK)
  2. Choose fraction/decimal display, check, and mode
  3. Switch views: recommended, elimination, substitution, graph

Examples

Result summary

All input and math stay in your browser; nothing is sent to servers.

Elimination is recommended because coefficients align easily.

Check

FAQ

When should I pick elimination vs substitution?

If any coefficient is 1 or -1, substitution is simpler. Otherwise, try elimination after aligning coefficients with the least common multiple.

Why is it valid to multiply both equations by the same number?

Doing so does not change the solution set, so clearing denominators or aligning coefficients keeps the answers intact.

Why must I use parentheses when substituting?

Parentheses prevent sign and distribution mistakes. This tool always inserts them before substitution.

How do you detect no solution or infinite solutions?

When the determinant is zero, mismatched constants imply parallel lines (no solution), while matching ratios imply overlapping lines (infinite solutions). The graph reflects the same classification.

Are fraction and decimal answers exact?

Yes. We keep exact rationals internally. Finite decimals are shown precisely; repeating decimals include an ≈ with limited digits.

Is anything sent to servers?

No. Only when you copy a share URL are equations and settings placed into the URL query.

Comments

Loaded only on demand. Until you click, no external request is made.