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Chapter 5: Q. 288 (page 672)

In the following exercises, solve each system by graphing.

x+2y<4y<x-2

Short Answer

Expert verified

The solution set is the region shaded with a darker color.

Step by step solution

01

Step 1. Given Information

The given system isx+2y<4y<x-2.

02

Step 2. Plot the first inequality

  • To plot the inequality x+2y<4, draw the dashed line x+2y=4because the inequality sign does not includes equality.
  • The point (0,0) satisfies the inequality, so shade the region that includes the origin.

03

Step 3. Plot the second inequality

  • To plot the inequality y<x-2, draw the dashed line y=x-2because the inequality sign does not includes equality.
  • The point (0,0)does not satisfies the inequality, so shade the region that does not include the origin.

  • The solution set is the region shaded with a darker color.
04

Step 4. Check the solution

  • One of the points that lie in the solution set is (0,-4).
  • Check if the point satisfies the inequalities.

0+2(-4)<?4-8<4-4<?0-2-4<-2

  • As both the inequalities are satisfied, the solution is verified.

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