Question

exit ticket
a system of inequalities is shown.
$x < 3$
$y \geq -3$
which graph represents the solution set?
(there are four graphs shown with coordinate planes, dashed and solid lines, etc.)

Explanation:

Step1: Analyze \( x < 3 \)

The inequality \( x < 3 \) means we draw a dashed vertical line at \( x = 3 \) (since it's a strict inequality, not \( \leq \)) and shade the region to the left of this line.

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

The inequality \( y \geq - 3 \) means we draw a solid horizontal line at \( y=-3 \) (since it's a non - strict inequality, \( \geq \)) and shade the region above this line.

Step3: Match with the graphs

We need to find the graph where there is a dashed vertical line at \( x = 3 \) (left - shaded) and a solid horizontal line at \( y=-3 \) (above - shaded). Looking at the options, we check the position of the vertical line (\( x = 3 \), dashed) and the horizontal line (\( y=-3 \), solid) and the shaded regions. The correct graph should have the dashed line at \( x = 3 \) (so vertical line at \( x = 3 \), dashed) and the solid line at \( y=-3 \) with the region above \( y = - 3 \) and to the left of \( x = 3 \) shaded. Among the given graphs, we identify the one that satisfies these two conditions.

Answer:

(Assuming the second graph (the one labeled with the second circle) is the correct one based on the analysis. If we consider the standard graph for \( x<3 \) (dashed vertical line at \( x = 3 \), left - shaded) and \( y\geq - 3 \) (solid horizontal line at \( y=-3 \), above - shaded), the graph with the dashed line at \( x = 3 \) and solid line at \( y=-3 \) with the correct shading. If we number the graphs from left to right as 1, 2, 3, 4, the second graph (graph 2) is the one that should represent the solution set. So the answer is the second graph (the one with the second circular marker).)