Question

look at the following system of inequalities:
$-3x + y > -2$
$2y \geq x + 2$
which graph represents the solutions to the system of inequalities?

Explanation:

Step1: Rewrite inequalities to slope-intercept

First inequality: $-3x + y > -2 \implies y > 3x - 2$
Second inequality: $2y \geq x + 2 \implies y \geq \frac{1}{2}x + 1$

Step2: Identify line styles

• $y > 3x - 2$: Dashed line (strict inequality), shade above.
• $y \geq \frac{1}{2}x + 1$: Solid line (non-strict), shade above.

Step3: Match to graphs

• Graph A: Dashed line is $y > 3x - 2$, solid line is $y \geq \frac{1}{2}x + 1$, overlapping shaded region is above both lines, matching the inequalities.
• Graph B: Shaded region is below both lines, which does not match.

Answer:

A (the top graph with overlapping shaded region above the dashed line $y=3x-2$ and solid line $y=\frac{1}{2}x+1$)