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GRAPH LINEAR INEQUALITIES IN TWO VARIABLES January 22, 2014 Pages 405-408

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SOLUTION Which ordered pair is not a solution of x – 3y ≤ 6? A (0, 0) B (6, – 1) C (10, 3) D (– 1, 2) Check whether each ordered pair is a solution of the inequality. Test (0, 0): x – 3y ≤ 6 0 – 3(0) ≤ 6 Write inequality. Substitute 0 for x and 0 for y. Simplify. 0 ≤ 6

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Test (6, – 1): x – 3y ≤ 6 6 – 3(– 1) ≤ 6 Substitute 6 for x and – 1 for y. Write inequality. Simplify. So, (0, 0) is a solution of x – 3y ≤ 6 but (6, – 1) is not a solution. ANSWER The correct answer is B. A B C D 9 ≤ 6

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SOLUTION Tell whether the ordered pair is a solution of – x + 2y < 8. Check whether each ordered pair is a solution of the inequality. Test (0, 0 ) – x + 2y < 8. 0 + 2(0) < 8 Write inequality. Substitute 0 for x and 0 for y. Simplify. (0, 0) 0 < 8 ANSWER So, (0, 0) is a solution of – x + 2y < 8.

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Graph the inequality y > 4x – 3. SOLUTION Graph the equation y = 4x – 3. The inequality is >, so use a dashed line. STEP 1 STEP 2 0 > 4(0) – 3 ? Test (0, 0) in y > 4x – 3. 0 >–3 Shade the half-plane that contains (0, 0), because (0, 0) is a solution of the inequality. STEP 3

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Graph the inequality x + 2y ≤ 0 SOLUTION STEP 1 Graph the equation x + 2y = 0. The inequality is <, so use a solid line. STEP 2 Test (1, 0) in x + 2y ≤ 01 1 + 2(0) ≤ 0 ? Shade the half-plane that does not contain (1, 0), because (1, 0) is not a solution of the inequality. STEP 3

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Graph the inequality x + 3y ≥ –1 SOLUTION STEP 1 Graph the equation x + 3y = –1. The inequality is <, so use a solid line. STEP 2 Test (1, 0) in x + 3y ≥ –1 1 + 3(0) ≥ –1 ? 1

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STEP 3 Shade the half-plane that contain (1, 0), because (1, 0) is a solution of the inequality.

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HOMEWORK WORKSHEET P 6.7

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