Chapter 6, Problem 55SGR

To determine

To graph : To solve the below mentioned inequalities by graphing:

  $y<3x-1$

And $y\ge -2x+4$

Explanation of Solution

Given information :

Given the two inequalities:

  $y<3x-1$

  $y\ge -2x+4$

Graph : The graph plotted below using the inequalities:

  $y<3x-1$

  $y\ge -2x+4$

Equation $y<3x-1$ is represented by light red area in above graph.

And $y\ge -2x+4$ is represented by light blue area in above graph.

Interpretation : >From the above graph, we see that $y<3x-1$ is the bottom area of line $y=3x-1$ (excluding line $y=3x-1$ ) which has been represented in light red. And we see that $y\ge -2x+4$ is the above area of the line $y=-2x+4$ (including the value of $y=-2x+4$ ) which has been represented in the light blue area.

So final solution is common color area which is in dark blue color. It covers the area bottom to $y=3x-1$ and above to $y=-2x+4$ and excluding point of intersection of the lines.