“Where the Points Lie” Systems of Linear Inequalities

Systems of Inequalities Standard Form Guided Practice Graph 2x + 3y 12 and shade the solution set. To review methods of graphing inequalities from standard form, graph 2x + 3y 12 by solving the inequality for y.

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

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

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

Systems of Inequalities Standard 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 > 12 This is not true, so shade on the side opposite the test point.

Systems of Inequalities Standard Form Review Shade the intersection of the two solution sets.