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Chapter 5: Q. 301 (page 672)

In the following exercises, solve each system by graphing.

3x-4y<8x<1

Short Answer

Expert verified
  • The solution set of the system is the area shaded in darker color excluding the boundary.

Step by step solution

01

Step 1. Given information

The given system is3x-4y<8x<1.

02

Step 2. Plot the first inequality 

  • The intercepts of 3x-4y=8are (0,-2),83,0.
  • Join the points to plot a dotted 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 x=1will be a vertical line passing through (1,0).
  • Draw a dotted vertical 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 excluding the boundary.
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.

-3-4<?8-7<8

-1<1

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

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