#  Linear Equations in Two Variables  To Graph a Linear Inequality 1)Graph the related linear equality (forms the boundary line).  and  are graphed.

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 Linear Equations in Two Variables

 To Graph a Linear Inequality 1)Graph the related linear equality (forms the boundary line).  and  are graphed as solid lines are graphed as dashed lines 2)Choose a point not on the boundary line & substitute into original inequality. If a true statement results, shade the half-plane containing the point. If a false statements results, shade the half-plane that does NOT contain the point. Linear Equations in Two Variables

x y Pick a point not on the graph: (0,0) (0, 0) Example 1

Linear Equations in Two Variables Graph 3 x + 5 y  –2 x y Pick a point not on the graph: (0,0), but just barely Graph 3 x + 5 y = –2 as a solid line. Test it in the original inequality. 3(0) + 5(0)  – 2 0  – 2 False, so shade the side that does not contain (0,0). (0, 0) Example 2

Linear Equations in Two Variables Graph 3 x < 15 x y Pick a point not on the graph: (0,0) Graph 3 x = 15 as a dashed line. Test it in the original inequality. 3(0) < 15 0 < 15 True, so shade the side containing (0,0). (0, 0) Example 3

 Note that although all of our examples allowed us to select (0, 0) as our test point, that will not always be true. If the boundary line contains (0,0), you must select another point that is not contained on the line as your test point. Linear Equations in Two Variables Warning!

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