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Chapter 5: Q. 300 (page 672)

In the following exercises, solve each system by graphing.

y≤-12x+3y<1

Short Answer

Expert verified
  • The solution set of the system is the area shaded in darker color including the solid line.

Step by step solution

01

Step 1. Given Information

The given system isy≤-12x+3y<1.

02

Step 2. Plot the first inequality

  • The intercepts of y=-12x+3are (0,3),(6,0).
  • 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 line y=1will be a horizontal line passing through (0,1).
  • Draw a dotted horizontal line on the same graph.
  • The point (0,0)satisfies the inequality, so shade the region that includes the origin.

  • The solution set of the system is the area shaded in darker color including the solid line.
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 the point (0,0)satisfies both the inequalities.
  • As both the inequalities are satisfied, the solution is verified.

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