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Chapter 5: Q. 5.112 (page 668)

Solve the system by graphing.

y鈮�-14+2x+4y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 second inequality.

Step by step solution

01

Step 1. Given Information

The given system isy鈮�-14+2x+4y鈮�4.

02

Step 2. Plot the first inequality 

  • The intercepts of y=-14x+2are (0,2),(8,0).
  • 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 x+4y=4are (0,1),(4,0).
  • 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 color. It is 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 (0,0).
  • It has already been checked that this point satisfies both the inequalities.
  • As both the inequalities are satisfied, the solution is verified.

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