QUICK LINKS


Introduction

QUICK LINKS


Introduction

Solving Systems of Linear Inequalities

INTRO
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A system of linear inequalities is a set of two or more linear inequalities.

We can solve a system of linear inequalities by graphing each inequality and identifying where the shaded areas overlap.

If you’d like to review how to graph a linear inequality, check out our lesson!

If we imagine that the shaded area for each inequality represents safety from a specific monster, then the space where all the shaded areas overlap represents the area we’re completely safe and contains the solutions to the system of inequalities.

Select the safe Brains. If none are safe, just press Check!

Remember, a solid line means the boundary is also safe, and a dotted line means the boundary is not safe.

How do we check if a point is a solution to a system of linear inequalities?

We can plug in the and values of the point into each linear inequality and simplify.

System

If all of the inequalities simplify to a true statement, then the point is a solution.

Point: βœ…

If one or more of the inequalities simplify to a false statement, then the point is not a solution.

Point: ❌
Check out our
Calculator
or explore our
Lesson
and
Practice
sections to learn more about solving systems of linear equations by graphing and test your understanding.

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CALCULATOR
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Systems of Linear Inequalities Calculator

KEY STEPS
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How to Solve a System of Linear Inequalities

Step 1. Graph the first inequality.

Step 2. Graph the second inequality.

Step 3. Identify the possible solutions.

The points inside the area where the inequalities overlap and on any solid boundaries of the area represents all the possible solutions.
LESSON
β€” Solving Systems of Linear Inequalities
PRACTICE
β€” Solving Systems of Linear Inequalities
CONCLUSION
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