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

Answer:

The graph is shown below.

Step-by-step 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.