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Chapter 5: Q. 299 (page 672)

In the following exercises, solve each system by graphing.

y≥34x-2y<2

Short Answer

Expert verified

The solution set of the system is the region shaded in the darker color including the boundary lines.

Step by step solution

01

Step 1. Given Information

The given system isy≥34x-2y<2

02

Step 2. Plot the first inequality 

  • The intercepts of y=34x-2are 83,0,(0,-2).
  • 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 line y=2will be a horizontal line passing through (0,2).
  • Draw a vertical line that is solid on the same graph.
  • The point (0,0)satisfies the inequality, so shade the region that includes the origin.

04

STep 4. Check the Solution

  • One of the points that lie in the solution set is (0,0).
  • It has already been verified that(0,0)satisfies both the inequalities.
  • As both the inequalities are satisfied, the solution is verified.

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