Question

question 2 of 10
identify the graph and describe the solution set of this system of inequalities.
$y > \frac{1}{3}x + 5$
$y < \frac{1}{3}x - 1$
\bigcirc a. there is no solution.
graph with regions a, b, c

Explanation:

Step1: Analyze the slopes and intercepts

The two inequalities are \( y > \frac{1}{3}x + 5 \) and \( y < \frac{1}{3}x - 1 \). Both lines have the same slope \( m=\frac{1}{3} \), so they are parallel. The y - intercept of the first line is \( 5 \) (from \( y=\frac{1}{3}x + 5 \)) and the y - intercept of the second line is \( - 1 \) (from \( y=\frac{1}{3}x-1 \)).

Step2: Analyze the regions

For the inequality \( y > \frac{1}{3}x + 5 \), the solution region is above the line \( y=\frac{1}{3}x + 5 \). For the inequality \( y < \frac{1}{3}x - 1 \), the solution region is below the line \( y=\frac{1}{3}x - 1 \). Since the line \( y=\frac{1}{3}x + 5 \) is above the line \( y=\frac{1}{3}x - 1 \) (because \( 5>-1 \) and they are parallel), there is no overlap between the region above \( y=\frac{1}{3}x + 5 \) and the region below \( y=\frac{1}{3}x - 1 \).

Answer:

A. There is no solution.