Question

on to a system of linear inequalities is the d pairs that satisfy all the linear inequalities. olution can be shown by graphing. ade each linear inequality. o the system is where the shading overlaps. lies. clearly indicate the solution region. 2. $y \leq \frac{3}{4}x - 4$ $y > -7$

Explanation:

Step1: Graph boundary $y=\frac{3}{4}x-4$

This is a line with slope $\frac{3}{4}$ and y-intercept $-4$. Since the inequality is $y\leq\frac{3}{4}x-4$, draw a solid line (because equality is allowed) and shade the region below the line.

Step2: Graph boundary $y=-7$

This is a horizontal line passing through $y=-7$. Since the inequality is $y>-7$, draw a dashed line (because equality is not allowed) and shade the region above this line.

Step3: Identify overlapping shaded region

The solution to the system is the area that is shaded in both Step1 and Step2.

Answer:

The solution region is the area that lies below the solid line $y=\frac{3}{4}x-4$ and above the dashed line $y=-7$, with overlapping shading clearly marked.