Solving by Substitution

Solving by substitution means isolating a variable in one equation, substituting into the other, solving the single-variable result, back-substituting, and checking the pair in both originals.

Solve x + y = 7 with x − y = 3. Isolate: y = 7 − x. Substitute: x − (7 − x) = 3, so 2x − 7 = 3 and x = 5. Back-substitute: y = 7 − 5 = 2. The candidate is the pair (5, 2), and the check runs in both originals: 5 + 2 = 7 and 5 − 2 = 3 — two equations, two receipts. Isolate the easiest variable available; a coefficient of 1 keeps fractions out of the pipeline, and any choice lands on the same pair.