Math 1 · Unit 6 · Lesson 3
Solving by Elimination
Line the two equations up and add them so one variable cancels. To make that happen, multiply one or both equations so the variable has opposite coefficients, additive inverses that add to 0, the make-a-zero-appear idea from Unit 1. Adding two true equations gives another true one. Then one variable is left, and it is a Unit 1 equation.
The big idea
Elimination adds two true equations to get a third true equation with one variable gone. It works because adding equal things to equal things keeps things equal, and the variable disappears because its two terms were chosen to be opposites, additive inverses that add to zero, the same make-a-zero-appear idea that started Unit 1. When the coefficients are not opposites yet, multiply one or both equations by a number, both sides, so they become opposites. Then solve the one-variable equation, back-substitute into either original, and check the pair in both. Graphing shows, substitution swaps, elimination adds, and every one of them turns two variables into one.
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 idea, why adding is allowed, the five steps, multiplying one or both, and which method to choose. Plus a worksheet with an answer key and a short lesson plan.