Two equations, two unknowns. The elimination method adds or subtracts the equations to cancel a variable. Substitution takes a different route: get one variable on its own in one equation, then put that expression in place of the variable in the other. Two unknowns become one.

Take this pair:

The first equation already has y by itself, so it tells us exactly what y is worth: substitute 2x - 1 for y in the second equation and only x is left.

The recipe is always the same:

1. Isolate one variable in one equation — make it the subject (this is just rearranging the formula).
2. Substitute that expression into the other equation.
3. Solve the single-variable equation you now have.
4. Back-substitute that value to find the second variable.

Pick whichever variable is already alone — or easiest to isolate — so you avoid fractions. Here y is already the subject, so substitution is the natural choice.

See it solved

Step through the four moves on our pair — isolate, substitute, solve, back-substitute.

See it explained

Sal Khan works a system by substituting one equation into the other.