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Chapter 5: Q. 314 (page 673)

In the following exercises, solve each system by graphing.

y<34x-2-3x+4y<7

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<34x-2-3x+4y<7.

02

Step 2. Plot the first inequality

  • To plot the inequality y<34x-2, draw the dotted line y=34x-2because 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.

03

Step 3. Plot the second inequality

  • To plot the inequality -3x+4y<7, draw the dotted line -3x+4y=7because the inequality sign does not include 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 (5,0).
  • Check if the point satisfies the inequalities.

0<?34(5)-20<?154-20<74-3(5)+4(0)<?7-15<7

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

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