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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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