Math 1 · Unit 6 · Lesson 1
What a System Is, and Solving by Graphing
A system of equations is two lines at once, and a solution is the one point on both: where they cross. Graph both lines from m and b, read the crossing point, and check it in both equations. Graphing lets you see the answer; the next two lessons give exact answers by algebra.
The big idea
A system of equations is two or more equations that must all be true at the same time, and a solution is a point that works in every one of them. For two lines, that is the intersection: the one place both lines share the same x and the same y. Solving by graphing is Unit 3 twice: graph each line from m and b, read the crossing, and check the point in both equations. It is the best way to see what a solution means, and its limit is honest: a crossing that is not on a grid corner cannot be read exactly, which is why the next two lessons give exact answers by turning 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 what a system is, the graphing method, the check, and the honest limit. Plus a worksheet with grids and an answer key, and a short lesson plan.