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Chapter 5: Q. 286 (page 672)

In the following exercises, solve each system by graphing.

y鈮�-23x+2y>2x-3

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�-23x+2y>2x-3.

02

Step 2, Plot the first inequality

  • To plot the inequality y鈮�-23x+2, draw the solid line y=-23x+2because the inequality sign 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>2x-3, draw the dotted line y=2x-3because the inequality sign does not 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 (0,3).
  • Check if the point satisfies the inequalities.

3鈮�?-23(0)+23鈮�?0+23鈮�23>?2(0)-33>-3

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

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