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4.2.1 – Linear Inequalities with Two Variables

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Recall, we have address linear inequalities so far with just one variable Solved them similar to equations, then graphed their solutions on a number line However, most instances, our inequalities will have 2-variables

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When given two variables, we can solve similar to equations we have before, especially those in standard form – Ax + By = C

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The different forms of linear inequalities with two variables may include Ax + By < C Ax + By ≤ C Ax + By > C Ax + By ≥ C

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Verifying Solutions To check answers, we will pick points, or substitute certain values, and see if the statement is true – If true, good to go – If not, then points are not a solution

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Example. Tell whether the following ordered pairs are a solution to the inequality 2x + y < 5. A) (1, 4) B) (2, -1) C) (0, 6)

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Graphing Inequalities With inequalities, in one or two variables, we can graph their solution/solution sets in the Cartesian plane Unlike lines, however, when we graph inequalities, there are different rules for situations

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Type of Line/Shading First thing is the type of line >, < = Use a dashed line (air underneath the symbol, air on the line) ≥, ≤ = Solid line (bar underneath the symbol, bar for the line)

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Shading When graphing the inequalities, we will shade a particular region on the graph The shading depends on the sign orientation >, ≥ = Shade above the line OR to the right (for vertical lines) <, ≤ = Shade below the line OR to the left (for vertical lines)

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Example. Graph the inequality x > -4 Type of line? Shading?

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Example. Graph the inequality y ≤ -4 Type of line? Shading?

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Example. Graph the inequality y ≥ 2 Type of line? Shading?

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Example. Graph the inequality -x ≥ 6 Type of line? Shading?

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Assignment Pg. 182 4-15, 16-28 even

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