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Chapter 5: Q. 285 (page 672)

In the following exercises, solve each system by graphing.

y<2x-1y鈮�-12x+4

Short Answer

Expert verified

The solution set is the region shaded with a darker color.

Step by step solution

01

Step 1. Given Information

The given system isy<2x-1y鈮�-12x+4.

02

Step 2. Plot the first inequality 

  • To plot the inequality y<2x-1, draw the dotted line y=2x-1because the inequality sign does not includes equality.
  • The point (0,0)does not satisfies the inequality, so shade the region that does not includes the origin.

03

Step 3. Plot the second inequality  

  • To plot the inequality y鈮�-x2+4, draw the solid line y=-x2+4because the inequality sign includes equality.
  • The point (0,0)satisfies the inequality, so shade the region that includes the origin.

  • The solution set is the region shaded with a darker color.
04

Step 4. Check the solution

  • One of the points that lie in the solution set is (2,0).
  • Check if the point satisfies the inequalities.

0<?2(2)-10<?4-10<30鈮�?-12(2)+40鈮�?-1+40鈮�3

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

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