Question

which graph represents the solution set of the system of inequalities? (is my selected answer correct, if not please help!!)

Answer 1

the graph on the right-top

Explanation:

Transferring an "x" to the right side in
`x+y\ge-3`, we get
`y\ge -x-3`

The system of inequalities is

`\left \{ {{y<2x+2} \atop {y\ge -x-3}} \right.`

We have y=2x+2 - ascending function with a=2, b=2

b=2 shows that ascending function intersects Y-axis is in y=2 - that situation is only on the right-top and left-down. So, we refuse left-top and right-down.

y=-x-3 - descending function with a=-1, b=-3

y<2x+2 is an area below the ascending function and we see that on the left-

`y\ge-x-3` is an area above the descending function

On the left-down we have an area above both functions, so we refuse this picture

Right-top is correct