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Chapter 5: Q. 284 (page 672)

In the following exercises, solve each system by graphing.

y<-2x+2y鈮�-x-1

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 isy<-2x+2y鈮�-x-1.

02

Step 2. Plot the first inequality 

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

03

Step 3. Plot the second inequality 

  • To plot the inequality y鈮�-x-1, draw the solid line y=-x-1because the inequality sign includes equality.
  • The point (0,0)satisfies the inequality, so shade the region that includes 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 (-5,5).
  • Check if the point satisfies the inequalities.

5<?-2(-5)+25<?10+25<125鈮�?-(-5)-15鈮�?5-15鈮�4

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

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