Question

which graph shows the solution to this system of inequalities?
$y < 2x + 4$
$y \geq -x - 3$
answer options
graph w
graph x
graph y
graph z
a. graph w
b. graph x
c. graph y
d. graph z

Explanation:

Step1: Analyze \( y < 2x + 4 \)

The inequality \( y < 2x + 4 \) has a dashed line (since it's \( < \), not \( \leq \)) with slope \( 2 \) and y - intercept \( 4 \). The region below the line is shaded.

Step2: Analyze \( y \geq -x - 3 \)

The inequality \( y \geq -x - 3 \) has a solid line (since it's \( \geq \)) with slope \( - 1 \) and y - intercept \( - 3 \). The region above the line is shaded.

Step3: Match with graphs

• Graph W: Incorrect shading for \( y < 2x + 4 \) (shaded below but the other inequality's shading doesn't match).
• Graph X: Dashed line for \( y < 2x + 4 \) (correct), solid line for \( y \geq -x - 3 \) (correct), and shading is the intersection of below \( y = 2x + 4 \) and above \( y=-x - 3 \).
• Graph Y: Incorrect line types (dashed for the wrong inequality) and shading.
• Graph Z: Incorrect shading and line types.

Answer:

B. Graph X