Substitution Method Calculator
Substitution method calculator shows you step-by-step how to solve systems of linear equations using the substitution method.
Solutionx = 2, y = 1
x2
y1
Determinant-3non-zero, so the solution is unique
Check equation 15 = 5
Check equation 21 = 1
By elimination
| Determinant | 2×-1 − 1×1 = -3 |
| x (Cramer) | (5×-1 − 1×1) ÷ -3 = 2 |
| y (Cramer) | (2×1 − 1×5) ÷ -3 = 1 |
The method
a₁x + b₁y = c₁ and a₂x + b₂y = c₂
Three possible outcomes
Two straight lines either cross once, run parallel and never meet, or coincide entirely. The determinant a₁b₂ − a₂b₁ distinguishes them: non-zero means a unique solution, zero means either none or infinitely many depending on the constants.
Elimination, substitution and Cramer’s rule all reach the same answer; they differ only in bookkeeping.