Cogito
Integrated Math 1 · Chapter 3 · Lesson 3
Systems of Inequalities
A region rather than a point.
12 problems · about 21 minutes · A-REI.D.12
What this lesson teaches
The student graphs systems of linear inequalities and identifies the solution region.
- An inequality shades half the plane on one side of a boundary line.
- Solid lines include the boundary; dashed lines exclude it.
- A system is solved by the region where every shading overlaps.
Warm Up
Straightforward practice. Get the method working first.
5 problemsDoes (0, 0) satisfy y ≤ 3x − 4? 1 yes, 0 no.
Answer 0
Why No.
What is the solution to a system of inequalities?
Answer The region where all the shaded areas overlap.
Why The overlapping region.
For y > x + 1, solid or dashed boundary? 1 solid, 2 dashed.
Answer 2
Why No equality included.
For y ≤ 4x, solid or dashed? 1 or 2.
Answer 1
Why Equality is included.
Does (0, 0) satisfy y > x + 3? 1 yes, 0 no.
Answer 0
Why 0 > 3 is false.
Build It Up
The same ideas with more to keep track of.
3 problemsDoes (0, 0) satisfy y < 5 − x? 1 yes, 0 no.
Answer 1
Why 0 < 5.
Does (2, 3) satisfy y ≥ x? 1 yes, 0 no.
Answer 1
Why 3 ≥ 2.
How many inequalities must a solution point satisfy in a system of three?
Answer 3
Why All of them.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsPut the graphing steps in order.
Answer 1. Graph the boundary line. 2. Make it solid or dashed based on the symbol. 3. Test a point not on the line. 4. Shade the side that satisfies the inequality.
Why The line comes before the shading.
Does (1, 1) satisfy y < 2x? 1 yes, 0 no.
Answer 1
Why 1 < 2.
The Test: Does the origin satisfy y < 2x + 1? 1 yes, 0 no.
Answer 1
Why Yes.
The Line: For y ≥ 3x − 2, is the boundary line solid or dashed? 1 solid, 2 dashed.
Answer 1
Why Solid.