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Solving Systems of Inequalities by Graphing Chapter 3.3

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Systems of Inequalities To solve a system of inequalities, you must find the ordered pairs that satisfy all of the inequalities in the system – Graph all inequalities on the same plane – The solution is the intersection of the graphs

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Example 1 y > 2x - 3 y < -x +2 Graph one inequality at a time – Lightly shade the appropriate regions Darken the region that has been shaded for both inequalities y > 2x - 3 y < -x + 2

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Example 2 y < -x +1 y < |x +1| Graph one inequality at a time – Lightly shade the appropriate regions Darken the region that has been shaded for both inequalities y < -x +1 y < |x + 1|

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Example 3 y > -3/4x + 2 y < -3/4x - 2 Graph one inequality at a time – Lightly shade the appropriate regions Darken the region that has been shaded for both inequalities – There is no intersection, therefore there is no solution y > -3/4x +2 y < -3/4x - 2

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