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, ameans the boundary is also , and a means the boundary is .
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.
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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