Substitution Method Calculator
Solve a 2×2 linear system by substitution.
The substitution method solves a system by isolating one variable and plugging it into the other equation.
The math behind it
From a₁x + b₁y = c₁, express x = (c₁ − b₁y)/a₁, substitute into the second equation and solve for y, then back-substitute for x. The result equals Cramer's rule.
Worked example
x + 2y = 5 and 3x − y = 1 → x = 1, y = 2.
FAQ
When is substitution easiest?
When one variable already has a coefficient of 1, so isolating it avoids fractions.