Home/Integrated Math 1/Lesson 88

Solve systems of linear inequalities by graphing

Find feasible regions by overlapping shaded half-planes.

Do this: Read the concept below, then try the quiz or activity.

Lesson 88 of 192
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Concept

Objective: Students will graph and interpret solution regions for systems of linear inequalities.

Estimated Time: 12 minutes

Standards:
HSA-REI.D.10HSF-IF.C.7

Graph each inequality and shade its solution region. The system solution set is the overlapping region.

Try it

Graph y ≥ x - 2 and y < -x + 4. Describe the feasible region.

📈 Coordinate Grapher

Use shaded inequalities to locate and verify the feasible region.

y = y = 1x
-10-9-8-7-6-5-4-3-2-112345678910-10-9-8-7-6-5-4-3-2-112345678910

Concept Check

System-inequality solutions appear where shading:

Concept Check

A strict inequality boundary is drawn as:

Common Misconception
Always verify your result in context instead of trusting a first pass.

Graph system inequalities

These steps are out of order — can you fix them?

1.Test a point in overlap
2.Find overlap region
3.Shade each valid side
4.Graph each boundary with correct line type

Short Answer

How can you verify a feasible-region point quickly?

Mastery Check

Pass this check with at least 80% to unlock completion.

Question 1

System-inequality solutions appear where shading:

Question 2

A strict inequality boundary is drawn as:

Pass the mastery check (80%+) to unlock completion.