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Chapter 5: Q. 294 (page 672)

In the following exercises, solve each system by graphing.

2x+y>-6-x+2y鈮�-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 is2x+y>-6-x+2y鈮�-4.

02

Step 2. Plot the first inequality

  • To plot the inequality 2x+y>-6, draw the dashed line 2x+y=-6because the inequality sign does not include 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+2y鈮�-4, draw the solid line -x+2y=-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.

2(1)+0>?-62>-6-(1)+2(0)鈮�?-4-1鈮�-4

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

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