Question

9 which graph best represents the solution set for the system of inequalities below?
$y \geq -\frac{4}{3}x + 3$
$y > \frac{1}{3}x - 2$
a
b
c
d

Explanation:

Step1: Analyze first inequality

The inequality is $y \geq -\frac{4}{3}x + 3$.

• The line $y = -\frac{4}{3}x + 3$ has a y-intercept of 3 and slope $-\frac{4}{3}$.
• The $\geq$ symbol means the line is solid, and we shade above the line.

Step2: Analyze second inequality

The inequality is $y > \frac{1}{3}x - 2$.

• The line $y = \frac{1}{3}x - 2$ has a y-intercept of -2 and slope $\frac{1}{3}$.
• The $>$ symbol means the line is dashed, and we shade above the line.

Step3: Find overlapping region

The solution set is the area shaded by both inequalities: above the solid line $y = -\frac{4}{3}x + 3$ and above the dashed line $y = \frac{1}{3}x - 2$. This matches graph C.

Answer:

C