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Chapter 5: Q. 5.109 (page 667)

Solve the system by graphing.

3x-2y鈮�12y鈮�32x+1

Short Answer

Expert verified

The solution set is the region shaded with the darker color and it is also the entire solution set of the second inequality.

Step by step solution

01

Step 1. Given Information

The given system is3x-2y鈮�12y鈮�32x+1.

02

Step 2. Plot the first inequality 

  • The intercepts of 3x-2y=12are (4,0),(0,-6).
  • Join the points to plot a solid line.
  • The point (0,0)satisfies the inequality, so shade the region that includes the origin.

03

Step 3. Plot the second inequality

  • The intercepts of y=32x+1are (0,1),-23,0.
  • Join the points to plot a solid line.
  • The point (0,0)does not satisfy the inequality, so shade the region that excludes the origin.

  • The solution set is the region shaded with the darker color and it is also the entire solution set of the second inequality.
04

Step 4. Check the Solution

  • One of the points that lie in the solution set is (-2,-2).
  • Check if the point satisfies the inequalities.

3(-2)-2(-2)鈮�?12-2鈮�12

-2鈮�?32(-2)+1-2鈮�-2

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

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