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“Where the Points Lie” Systems of Linear Inequalities

“Where the Points Lie” Systems of Linear Inequalities. Systems of Inequalities Standard Form Guided Practice. Graph 2x + 3y < 15 and 2x – 3y > 12 and shade the solution set.

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“Where the Points Lie” Systems of Linear Inequalities

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  1. “Where the Points Lie” Systems of Linear Inequalities

  2. Systems of InequalitiesStandard Form Guided Practice Graph 2x + 3y < 15 and 2x – 3y > 12 and shade the solution set. To review methods of graphing inequalities from standard form, graph 2x + 3y < 15 by finding the x-and y-intercepts and2x – 3y > 12 by solving the inequality for y.

  3. Systems of InequalitiesStandard Form Review Graph 2x + 3y < 15 using x- and y-intercepts. x-intercept is (x, 0) y-intercept is (0, y) 2(0) + 3y = 15 3y = 15 y = 5 (0, 5) 2x + 3(0) = 15 2x = 15 x = 7.5 (7.5, 0) Remember, the “greater than” and “less than” inequalities have dashed boundary lines.

  4. Systems of InequalitiesStandard Form Review Test a coordinate on either side of the line to see where to shade. Try (0, 0) 2(0) + 3(0) < 15 Substitute 0 + 0 < 15 Simplify 0 < 15 Simplify This is true, so shade on the side of the test point.

  5. Systems of InequalitiesStandard Form Review Graph 2x – 3y > 12 by solving the inequality for y. Test points to verify shading. (0, –4) What is the y-intercept? What is the slope? Is the boundary line dashed or solid?

  6. Systems of InequalitiesStandard Form Review Test a coordinate on either side of the line to see where to shade. Try (0, 0) 2(0) – 3(0) > 12 0 + 0 > 12 0 > 12 This is not true, so shade on the side opposite the test point.

  7. Systems of InequalitiesStandard Form Review Shade the intersection of the two solution sets.

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