Question

graph: $\begin{cases}y > 4x - 2\\y < -\frac{1}{2}x + 1end{cases}$

Explanation:

Step1: Graph $y = 4x - 2$

The line $y = 4x - 2$ has a y - intercept of - 2 and a slope of 4. Since the inequality is $y>4x - 2$, we draw a dashed line (because the inequality is strict) and shade the region above the line.

Step2: Graph $y=-\frac{1}{2}x + 1$

The line $y =-\frac{1}{2}x + 1$ has a y - intercept of 1 and a slope of $-\frac{1}{2}$. Since the inequality is $y<-\frac{1}{2}x + 1$, we draw a dashed line and shade the region below the line.

Step3: Find the intersection region

The solution of the system of inequalities is the region that is shaded for both inequalities, which is the region that is above $y = 4x - 2$ and below $y=-\frac{1}{2}x + 1$.

Answer:

The solution is the intersection of the region above the dashed line $y = 4x - 2$ and below the dashed line $y=-\frac{1}{2}x + 1$.