Question

What system of inequalities is represented by the graph? may you please tell me the correct answer and why

A coordinate graph is shown of overlapping areas formed by two lines.
The first line connects the points left-parenthesis 0 comma negative 1 right-parenthesis and left-parenthesis 1 comma 4 right-parenthesis. All coordinates to the right of this line are lightly shaded.
The second line connects the points left-parenthesis 0 comma 4 right-parenthesis and left-parenthesis 2 comma negative 2 right-parenthesis. All coordinates to the right of this line are also lightly shaded.
The region where the two gray shaded regions overlap is shaded darker.
(1 point)
Responses

y greater than or equal to negative 5 x minus 1 and y less than or equal to 3 x plus 4
Image with alt text: y greater than or equal to negative 5 x minus 1 and Image with alt text: y less than or equal to 3 x plus 4

y less than or equal to 5 x minus 1 and y greater than or equal to negative 3 x plus 4
Image with alt text: y less than or equal to 5 x minus 1 and Image with alt text: y greater than or equal to negative 3 x plus 4

y greater than or equal to 5 x minus 1 and y less than or equal to negative 3 x plus 4
Image with alt text: y greater than or equal to 5 x minus 1 and Image with alt text: y less than or equal to negative 3 x plus 4

y less than or equal to negative x plus 5 and y greater than or equal to 4 x minus 3

Answer 1

The correct answer is: y greater than or equal to negative 5 x minus 1 and y less than or equal to 3 x plus 4.

This is because the shaded region on the graph represents the area where both inequalities are true. The first line corresponds to y greater than or equal to negative 5 x minus 1, while the second line corresponds to y less than or equal to 3 x plus 4. When combined, the region where both of these conditions are met is shaded darkly on the graph.