Questions: Which system of inequalities represents the graph below? A) y ≤ -x + 4 and y > 5 B) y < -x + 4 and y ≤ 5 C) y ≥ -x + 4 and y < D) y ≥ -x + 4 and y ≥!

Transcript text: Which system of inequalities represents the graph below? A) $y \leq-x+4$ and $y>5$ B) $y<-x+4$ and $y \leq 5$ C) $y \geq-x+4$ and $y<$ ? D) $y \geq-x+4$ and $y \geq!$

Solution

Solution Steps

Step 1: Identify the boundary lines

The graph shows two boundary lines: one is a dashed line with a negative slope, and the other is a horizontal line. The dashed line represents the equation $ y = -x + 4 $, and the horizontal line represents $ y = 5 $.

Step 2: Determine the inequality for the dashed line

Since the region of interest is above the dashed line, the inequality for the dashed line is $ y \geq -x + 4 $.

Step 3: Determine the inequality for the horizontal line

The region of interest is below the horizontal line, so the inequality for the horizontal line is $ y \leq 5 $.