Math 1 · Unit 6 · Lesson 5
Systems of Inequalities
Two inequalities at once. Shade each one the Unit 5 way, with its own dashed or solid boundary and its own side, and the solution of the system is the overlap: the region shaded by both. A point is a solution only if it lands in the overlap, so it obeys both at the same time.
The big idea
A system of inequalities is two half-planes that must both hold. Shade each one exactly as in Unit 5, boundary from m and b, dashed or solid, the right side, and the solution of the system is the overlap, the region covered by both shadings. That is the same rule as every lesson in this unit: it has to work in every inequality, or it is not a solution. To test a point, put it into both; all true means it is in the overlap. The overlap keeps each boundary's own style, so a point on a dashed edge is left out. Unit 5 called the overlap the feasible region, and the next lesson puts real limits into it.
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 overlap idea, the four steps, testing a point in both, the edges, and a worked example. Plus a worksheet with grids and an answer key, and a short lesson plan.