Section 3.5 Linear Inequalities and Systems of Linear Inequalities in Two Variables 271 After graphing the solution to a linear inequality, we can verify that we have shaded the correct side of the line by using test points. In Example 1, we can pick an arbitrary ordered pair within the shaded region.Then substitute the x- and y-coordinates in the original inequality. If the result is a true statement, then that ordered pair is a solution to the inequality and suggests that other points from the same region are also solutions. For example, the point (0, 0) lies within the shaded region (Figure 3-10). Substitute (0, 0) in the original inequality. ✔ True The point (0, 0) from the shaded region is a solution. 3x y 1 3102 102 ? 0 0 ? 1 In Example 2, we will graph the solution set to a strict inequality. A strict inequality does not include equality and therefore is expressed with the symbols or . In such a case, the boundary line will be drawn as a dashed line. This indicates that the boundary itself is not part of the solution set. Graphing a Linear Inequality in Two Variables Graph the solution set. Solution: Solve for y. Because we divide both sides by a negative number, reverse the inequality sign. 54 4y 6 5x Graph the line defined by the related equation, y The boundary line is drawn as a dashed line because the inequality is strict. Also note that the line passes through the origin. Because the inequality is of the form the solution to the inequality is the region above the line. See Figure 3-11. y 5 4 3 1 Skill Practice Graph the solution set. 2. 3y 6 x y 7 mx b, x. y 7 5 4 x 4y 4 7 5x 4 4y 6 5x Example 2 1 Figure 3-11 x 1 2 3 4 5 5432 2 1 2 3 4 5 1 y 5 4 3 1 Figure 3-10 x 1 2 3 4 5 5432 2 1 2 3 4 5 Test point (0, 0) 1 y x 1 5 4 3 1 2 3 4 5 5432 2 1 2 3 4 5 1 Answer 2.
miller_intermediate_algebra_4e_ch1_3
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