Math 1 · Unit 6 · Lesson 2
Solving by Substitution
When one equation tells you what a variable equals, put that expression in place of the variable in the other equation. Two variables become one, and the one-variable equation is a Unit 1 problem. Back-substitute for the other variable, then check the pair in both. Exact answers, even fractions.
The big idea
Substitution is one swap and one Unit 1 equation. If one equation says what a variable equals, that expression can stand in for the variable in the other equation, because the solution point satisfies both equations at once, so the variable has the same value in both. After the swap there is one variable, and the equation is solved with the same moves as Unit 1. Back-substitute into the already-solved equation to get the other variable, then check the pair in both originals. Substitution fits best when a variable is already alone or has coefficient 1, and it gives the exact answer, fractions included, where a graph could only show about where.
The parts of this lesson
Each part is its own short page. Go in order, or pick the one you need.
Printables
One page with the why, the five steps, the parentheses warning, and a worked example. Plus a worksheet with an answer key and a short lesson plan.