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Chapter 5: Q. 313 (page 673)

In the following exercises, solve each system by graphing.

3y>x+2-2x+6y>8

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 is3y>x+2-2x+6y>8.

02

Step 2. Plot the first inequality

  1. To plot the inequality 3y>x+2, draw the dotted line 3y=x+2because the inequality sign doe snot include equality.
  2. The point (0,0)does not satisfy the inequality, so shade the region that does not include the origin.

03

Step 3. Plot the second inequality

  • To plot the inequality -2x+6y>8, draw the dotted line -2x+6y=8because the inequality sign does not include equality.
  • The point (0,0)does not satisfy 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 (0,5).
  • Check if the point satisfies the inequalities.

3(5)>?0+215>2-2(0)+6(5)>?830>8

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

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