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Chapter 5: Q. 311 (page 673)

In the following exercises, solve each system by graphing.

y鈮�-14x-2x+4y<6

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�-14x-2x+4y<6.

02

Step 2. Plot the first inequality

  • To plot the inequality y鈮�-14x-2, draw the solid line y=-14x-2because 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 x+4y<6, draw the dotted line x+4y=6because 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 (0,-5).
  • Check if the point satisfies the inequalities.

-5鈮�?-14(0)-2-5鈮�-20+4(-5)<?6-20<6

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

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