Question

ution of the given system.
\

$$\begin{cases} y > 2x \\\\ y = x + 2 \\end{cases}$$

tions.
solutions.
+1
8

1. \

$$\begin{cases} y > x - 4 \\\\ y < x + 2 \\end{cases}$$

Explanation:

Step1: Graph boundary line $y=x-4$

Draw a dashed line (since $y>x-4$ uses $>$) with slope $1$ and y-intercept $(0,-4)$.

Step2: Shade region for $y>x-4$

Shade the area above the dashed line $y=x-4$.

Step3: Graph boundary line $y=x+2$

Draw a dashed line (since $y

Step4: Shade region for $y

Shade the area below the dashed line $y=x+2$.

Step5: Identify overlapping region

The solution is the area where the two shaded regions overlap.

Answer:

The solution is the region between the two parallel dashed lines $y=x-4$ (dashed, lower line) and $y=x+2$ (dashed, upper line), including all points $(x,y)$ that satisfy both $y > x-4$ and $y < x+2$.

To plot this:

1. Plot the dashed line $y=x-4$ (passes through $(0,-4)$ and $(4,0)$)
2. Plot the dashed line $y=x+2$ (passes through $(0,2)$ and $(-2,0)$)
3. Shade the area between these two dashed lines.