Question

Which graph represents the solution set for the system 6x + y > -3 and 2x + y ≤ 4?

Answer 1

There was no graph options but this is what I got. 

Answer 2

The graph is shown below.

Explanation:

The given inequalities are

`6x + y > -3`

`2x + y \le 4`

The related line of both inequalities are

`6x + y=-3`

`2x + y = 4`

The table of values are

Line 1 Line 2

x y x y

0 -3 0 4

-0.5 0 2 0

Plot these ordered pairs on a coordinate plane and connect them by straight lines.

Check both inequalities by (0,0).

`6(0) + (0) > -3\Rightarrow 0>-3` True

`2(0) + (0) le 4\Rightarrow 0\le 4` True

It means (0,0) is included in the shaded region of both inequalities.

The feasible region is shown below.