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**3-3 Solving Systems of Inequalities by Graphing**

Objectives Students will be able to: 1) solve systems of inequalities by graphing 2) Determine the coordinates of the vertices of a region formed by the graph of a system of inequalities

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To solve a system of inequalities, we need to find the ordered pairs that satisfy all of the inequalities in the system. Steps: 1) Graph all inequalities on the same coordinate plane. 2) Look for the region on the coordinate plane that contains shading in common from all inequalities. This is the solution. 3) If there is no common shaded region, there is no solution.

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**Example 1: Solve each system of inequalities by graphing. a) **

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b)

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c)

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d)

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Try this. e)

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When graphing a system of linear inequalities that contains three or more inequalities, the solution to the system may be a region that is bounded on all sides, forming a polygon on the coordinate plane. You can find the vertices of the region by determining the coordinates of the points at which the boundary lines intersect. This is a very useful skill for Linear Programming (section 3-4).

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Example 2: Find the coordinates of the vertices of the figure formed by each system of inequalities. a)

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**Besides graphing, can you think of another way to find the vertices?**

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Try this b)

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-4 -3 -2 -1 0 1 2 3 4 4 3 2 1 -4 -3 -2 0 x y. -4 -3 -2 -1 0 1 2 3 4 4 3 2 1 -4 -3 -2 0 Example 1 x y X = 3.

-4 -3 -2 -1 0 1 2 3 4 4 3 2 1 -4 -3 -2 0 x y. -4 -3 -2 -1 0 1 2 3 4 4 3 2 1 -4 -3 -2 0 Example 1 x y X = 3.

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