Home/Integrated Math 1/Lesson 87

Is (x, y) a solution to the system of linear inequalities?

Check candidate points against every inequality in a system.

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

Lesson 87 of 192
45%

Concept

Objective: Students will evaluate points against systems of linear inequalities.

Estimated Time: 12 minutes

Standards:
HSA-REI.D.10HSA-CED.A.3

A point solves a system of inequalities only when it satisfies all inequalities simultaneously.

Try it

Determine whether (2,1) satisfies y ≥ x - 1 and y < 4.

📈 Coordinate Grapher

Graph both inequality regions and test points in the overlap.

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

A point is in the solution set when it satisfies:

Concept Check

If one inequality fails, the point is:

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

System-inequality point test

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

1.Conclude in/out
2.Evaluate truth values
3.Substitute into inequality 2
4.Substitute into inequality 1

Short Answer

Why can a point satisfy one inequality but not the system?

Mastery Check

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

Question 1

A point is in the solution set when it satisfies:

Question 2

If one inequality fails, the point is:

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