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

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.

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 $x $ and $y $ 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.

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

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