Chapter 5.7, Problem 38E

To determine

To find: the system of linear inequalities that has point $C$ and explain with reasoning.

Answer to Problem 38E

  $y>-3x+4\text{ and }y\le 2x+1$ .

Explanation of Solution

Given:

Concept used:

The difference is that a solution to the inequality is not the drawn line but area of the coordinate plane that satisfy the inequality.

The common area is the solution of inequality.

The boundary line is dashed for $<\text{or >}$ and solid line for $\le \text{or }\ge$ if the area is form above the line then the solution should be greater than line.

  $y>g\left(x\right)$ .

If the area is formed below the line then the solution or area formed is less than the line.

  $y<g\left(x\right)$ .

Calculation:

Consider the given graph;

Step $1$ : the line $y=-3x+4$ must have the shaded region above it because $B$ is not the solution, then the boundary line is dashed. For this use $>$ :

  $y>-3x+4$ .

Step $2$ : the line $y=2x+1$ must have the shaded region below it and since there are no points on this boundary line, for this use $\le$ :

  $y\le 2x+1$ .

Hence, $y>-3x+4\text{ and }y\le 2x+1$ .