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Chapter 5: Q. 312 (page 673)

In the following exercises, solve each system by graphing.

y鈮�3x-1-3x+y>-4

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鈮�3x-1-3x+y>-4.

02

Step 2. Plot the first inequality

  • To plot the inequality y鈮�3x-1, draw the solid line y=3x-1because the inequality sign 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 -3x+y>-4, draw the dotted line -3x+y=-4because 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 (-1,0).
  • Check if the point satisfies the inequalities.

0鈮�?3(-1)-10鈮�-4-3(-1)+0>?-43>-4

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

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