Question

period
y = -x + 2
y > -4x - 1

Explanation:

Step1: Find intersection of two lines

Set $-x + 2 = -4x -1$
$ -x +4x = -1 -2 $
$3x = -3$
$x = -1$
Substitute $x=-1$ into $y=-x+2$: $y = -(-1)+2=3$
Intersection point: $(-1, 3)$

Step2: Verify shaded region constraints

For $y\geq -x+2$: Shade above the solid line $y=-x+2$.
For $y > -4x -1$: Shade above the dashed line $y=-4x-1$.
The overlapping shaded region is the solution set, bounded by the two lines, above both, with the intersection at $(-1,3)$.

Answer:

The solution to the system of inequalities is the region that is above the solid line $y=-x+2$ and above the dashed line $y=-4x-1$, with the intersection point of the two lines at $(-1, 3)$. In set notation, this is $\{(x,y) \mid y\geq -x+2 \text{ and } y > -4x -1\}$.