Question

which graph represents this system of inequalities?
\

$$\begin{cases} y < -3x + 5 \\\\ y < x + 2 \\\\ y < -1 \\end{cases}$$

\bigcirc a. \quad \text{graph a}
\bigcirc b. \quad \text{graph b}
\bigcirc c. \quad \text{graph c}

Explanation:

Step1: Analyze line styles

All inequalities use $<$, so all boundary lines are dashed.

Step2: Graph $y < -3x + 5$

Boundary line: $y=-3x+5$ (slope $-3$, y-intercept $5$). Shade below the line.

Step3: Graph $y < x + 2$

Boundary line: $y=x+2$ (slope $1$, y-intercept $2$). Shade below the line.

Step4: Graph $y < -1$

Boundary line: $y=-1$ (horizontal line). Shade below this line.

Step5: Find overlapping region

The solution is the area shaded below all three dashed lines, which matches the region in Option A.

Answer:

A. <The graph with dashed lines $y=-3x+5$, $y=x+2$, $y=-1$, and the overlapping shaded region below all three lines>