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Chapter 5: Q. 5.111 (page 668)

Solve the system by graphing

y鈮�3x+1-3x+y鈮�-4

Short Answer

Expert verified
  • The solution set is the area on the graph shaded in a darker color. It is the entire solution set of the first inequality.

Step by step solution

01

Step 1. Given Information

The given system isy鈮�3x+1-3x+y鈮�-4.

02

Step 2. Plot the first inequality

  • The intercepts of y=3x+1are (0,1),-13,0.
  • 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.

03

Step 3. Plot the second inequality

  • The intercepts of -3x+y=-4are 43,0,(0,-4).
  • Join the points to plot a solid line.
  • The point (0,0)satisfies the inequality, so shade the region that includes the origin.

  • The solution set is the area on the graph shaded in a darker colur. It is the entire solution set of the first inequality.
04

Step 4. Check the Solution

  • One of the points that lie in the solution set is (-1,-1).
  • Check if the point satisfies the inequalities.

-1鈮�?3(-1)+1-1鈮�-2

-3(-1)-1鈮�?-42鈮�-4

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

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