The Substitution Strategy

Algebra 1 · Axiom Academy

LESSON The Substitution Strategy A step-by-step method for solving a system of equations: solve one equation for a variable, then substitute that expression into the other. Our goal is the single (x, y) pair that satisfies both equations at the same time. Picture each equation as a line: the solution is exactly the point where the two lines intersect. The method begins by getting one variable alone on one side of one equation. Here y is already isolated in y = x + 1 — so the whole expression x + 1 is a stand-in for y . Anywhere we see y , we may write x + 1 instead. This is the main event. Take the expression for the isolated variable, x + 1 , and drop it into the other equation in place of y . Two equations collapse into a single equation in just one variable. 4. Solve for the First Variable Now it's an ordinary one-variable equation. Combine the like x -terms, move the constant across, and divide — standard algebra leads straight to x . 5. Back-Substitute for the Second Variable Halfway home: we know x = 2 . Plug that value back into either original equation to recover y . The easiest is the one where y was already alone, y = x + 1 . We found x = 2 and y = 3 . The solution is the ordered pair built from those values — and it is exactly the point where the two original lines cross. You've solved a system end-to-end by substitution: isolate, substitute, solve, and back-substitute to land on the point where two lines meet. Scroll up to revisit any step.

This is the written version of the interactive lesson above. See the full Algebra 1 course.