Question

solve the system of inequalities by graphing.
$y > 5$
$y < x + 2$
a) graph
b) graph

Explanation:

Step1: Analyze \( y > 5 \)

The inequality \( y > 5 \) represents the region above the horizontal dashed line \( y = 5 \) (since the inequality is strict, the line is dashed).

Step2: Analyze \( y < x + 2 \)

The inequality \( y < x + 2 \) represents the region below the line \( y = x + 2 \) (the line has a slope of \( 1 \) and a \( y \)-intercept of \( 2 \), and it is dashed because the inequality is strict).

Step3: Find the Intersection

The solution to the system is the region that satisfies both inequalities, i.e., above \( y = 5 \) and below \( y = x + 2 \). We need to check which graph (A or B, though B's full graph isn't shown, but from the options, we analyze the key features) has the overlapping region of \( y > 5 \) (above \( y = 5 \)) and \( y < x + 2 \) (below \( y = x + 2 \)). The correct graph should have the area where \( y \) is greater than \( 5 \) and less than \( x + 2 \), which corresponds to the region that is above the horizontal line \( y = 5 \) and below the line \( y = x + 2 \). Assuming the options are structured such that the correct one shows this intersection, we identify the correct graph (though due to partial visibility, but based on the system, we conclude the correct region).

Answer:

(Assuming the correct option is the one with the overlapping region of \( y > 5 \) and \( y < x + 2 \), for example, if A is the one with the region above \( y = 5 \) and below \( y = x + 2 \), then) A (with the region above \( y = 5 \) and below \( y = x + 2 \))