Unit 7

Systems of Equations

Two equations, two unknowns: graphing, substitution, elimination, special cases

A single equation like y = 2x + 1 has a whole line of answers. Every point on that line fits it. This unit is about what happens when you have two equations that both have to be true at once. That second demand usually narrows things down to a single answer, the one pair of numbers that works for both.

Keep one picture in mind the whole way through. Each equation draws a line. A pair of equations is asking a simple question: is there one point that sits on both lines at once? When there is, it's the place the two lines cross. Everything in this unit, whether graphing or substitution or elimination, is just a different way to find that crossing point.

One habit never changes here. Once you have an answer, put it back into both equations and make sure both come out true.

It helps to have your work with single equations fresh. Before each new lesson, redo two or three problems from the lesson before from memory, then check them. Practice spaced out like that feels harder in the moment, and that's exactly what makes a skill last to next week. Every set in this unit has its answers at the end of the lesson, so the help is always right there.