Algebra Calculators
Two-Variable Equation Solver
Solve a system of two linear equations in x and y by Cramer's rule.
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What is Two-Variable System?
Two linear equations in two unknowns describe two lines on a plane, and solving them means finding where the lines meet: one point, no point (parallel) or every point (the same line).
How it works
Cramer's rule divides two determinants to give x and y. When the main determinant is zero the lines do not cross at a single point, and the tool distinguishes the two possibilities — proportional constants mean the same line (infinitely many solutions), otherwise the lines are parallel (none) — instead of silently returning NaN.
- Enter your input. Type or paste your input into the field above — the tool responds instantly.
- Review the result. Output updates live as you type. Everything runs entirely in your browser.
- Copy or download. Use the Copy button to grab the result, or Download to save it as a file.
Examples
Realistic sample
Type or paste any realistic input — the tool computes the result locally and instantly.
Common mistakes
Expecting a server round-trip
Nothing is uploaded — every tool in this category runs entirely in your browser.