Math 1 · Unit 6 · Lesson 5 · part 2 of 5
Two inequalities at once: the overlap
A system of inequalities is two or more inequalities that must all be true at once.
Two inequalities at once: the overlap
A system of inequalities is two or more inequalities that must all be true at once. Each one alone shades a half-plane (Unit 5). The solution of the system is the part shaded by every inequality: the overlap. A point is a solution only if it lands in the overlap, because only there does it obey both at the same time.
y ≤ x + 1 and y > −x + 3
- 1Shade the first inequalityThe Unit 5 procedure: solve for y, boundary from m and b, dashed or solid, shade the side, test a point.
- 2Shade the second one, in another colorSame procedure. Its own dashed or solid boundary, its own side.
- 3The overlap is the answerThe region covered by both colors. Its edges keep their own style: dashed where the boundary was dashed, solid where solid.
- 4Test a point in bothA point is a solution only if it makes both inequalities true.
It has to obey every inequality. The same rule as Lesson 1, in region form. Shaded by one is not enough; the solutions are where the shadings overlap. Unit 5 called this the feasible region, the allowed combinations.