Question

sketch the solution to this system of inequalities:
$y < 1$
$y > x - 2$
a)
image of a graph
b)
image of a graph
c)
image of a graph
d)
image of a graph

Explanation:

Step1: Analyze \( y < 1 \)

The inequality \( y < 1 \) represents the region below the horizontal line \( y = 1 \) (dashed line since it's \( < \), not \( \leq \)).

Step2: Analyze \( y > x - 2 \)

The inequality \( y > x - 2 \) represents the region above the line \( y = x - 2 \) (dashed line since it's \( > \), not \( \geq \)). The line \( y = x - 2 \) has a slope of \( 1 \) and a y - intercept of \( - 2 \).

Step3: Match with graphs

• For option A: The shaded region does not match the regions defined by \( y < 1 \) and \( y > x - 2 \).
• For option B: The shaded region is not below \( y = 1 \) and above \( y=x - 2\) correctly.
• For option C: The shaded region is below \( y = 1 \) (horizontal dashed line) and above \( y=x - 2\) (dashed line with slope 1, y - intercept - 2), which matches the system of inequalities.
• For option D: The lines and shaded region do not match the given inequalities.

Answer:

C