Question

1. $-4x + 3y < -9$

$-2x + 2y > -4$

Explanation:

Step1: Rewrite first inequality to slope-intercept form

Isolate $y$ in $-4x + 3y < -9$:
Add $4x$ to both sides: $3y < 4x - 9$
Divide by 3: $y < \frac{4}{3}x - 3$

Step2: Rewrite second inequality to slope-intercept form

Isolate $y$ in $-2x + 2y > -4$:
Add $2x$ to both sides: $2y > 2x - 4$
Divide by 2: $y > x - 2$

Step3: Identify boundary lines and shading

For $y < \frac{4}{3}x - 3$: Boundary is dashed line $y=\frac{4}{3}x-3$, shade below it.
For $y > x - 2$: Boundary is dashed line $y=x-2$, shade above it.

Step4: Find intersection of shaded regions

The solution is the overlapping shaded area of the two inequalities.

Answer:

The solution is the region where $y < \frac{4}{3}x - 3$ and $y > x - 2$, represented by the overlapping area below the dashed line $y=\frac{4}{3}x-3$ and above the dashed line $y=x-2$ on the coordinate plane.