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3.3: Graphing and Solving Systems of Linear Inequalities Intro: Systems of inequalities are similar to systems of equations. A solution is still an ordered pair that is true in both statements. The graphing is a little more sophisticated - its all about the shading.

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Graphing Method Example: Graph the inequalities on the same plane: x + y 4. Before we graph them simultaneously, lets look at them separately. Graph of x + y

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Graphing Method 4 This is: 2x - y > 4. So what happens when we graph both inequalities simultaneously?

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Coolness Discovered! 4 Wow! 4 The solution to the system is the brown region - where the two shaded areas coincide. 4 The green region and red regions are outside the solution set.

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So what were the steps? 4 Graph first inequality –Shade lightly (or use colored pencils) 4 Graph second inequality –Shade lightly (or use colored pencils) 4 Shade darkly over the common region of intersection. 4 That is your solution!

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Challenge Extended Graph y -3x -1 and y < x + 2

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What about THREE inequalities? 4 Graph x 0, y 0, and 4x + 3y 24 4 First off, lets look at x 0 and y 0 separately.

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Graphing THREE inequalities 4 Now lets look at x 0 and y 0 together. Clearly, the solution set is the first quadrant.

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Graphing THREE inequalities 4 So therefore, after we graph the third inequality, we know the solution region will be trapped inside the first quadrant. So lets look at 4x + 3y 24 by itself.

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Graphing THREE inequalities 4 Now we can put all of our knowledge together. 4 The solution region is the right triangle in the first quadrant.

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