Solve two simultaneous equations by elimination, with the working and a substitution check.
Solve a pair of simultaneous equations by elimination: the calculator multiplies one equation so a variable cancels, then back-substitutes. Shown step by step, including the no-solution and infinite-solution cases.
Solution
How to use this tool
Move all x and y terms to the left and the constant to the right.
a₁, b₁, c₁ for equation 1 and a₂, b₂, c₂ for equation 2.
The solution is the point where the two lines cross.
Both equations are re-evaluated with the answer shown.
Formula & worked example
x + y = 5 and x − y = 1: adding the equations eliminates y, giving 2x = 6, so x = 3; back-substituting gives y = 2. The check confirms 3 + 2 = 5 and 3 − 2 = 1.
Limitations — read this before you rely on it
Solves linear 2 × 2 systems only. It does not solve quadratics, three-variable systems or inequalities, and near-parallel lines can give very large, rounding-sensitive answers — check the substitution values if the determinant is close to zero.
Frequently asked questions
A way to solve simultaneous equations: multiply one equation so a variable has matching coefficients, then add or subtract the equations so that variable cancels, leaving one equation in one unknown.
Add them: 2x = 6, so x = 3. Put x = 3 into either equation: 3 + y = 5, so y = 2.
The two equations describe parallel lines that never meet — for example x + y = 2 and x + y = 5. The determinant is 0 and the constants disagree.
The two equations describe the same line — for example x + y = 2 and 2x + 2y = 4. Every point on the line works.
Yes. Coefficients may be any real numbers, including fractions entered as decimals and negative values.