Explanation:
i cannot draw here, but I can explain if to you.
first, for every inequality we need to find the limit between the points on the coordinate grid that are valid, and the ones that are not.
every point (x, y), for which the inequality is true, is a valid one. every point for which the inequality is false, is invalid.
for this we treat every inequality as equality (equation) with an "=" sign.
this gives us the delimiter line between the valid and invalid points.
3y > 2x + 12
turns into
3y = 2x + 12
y = (2/3)x + 4
it is a line that goes through
(0, 4) and then (0+3, 4+2) = (3, 6)
because the slope gives us the ratio
(y difference) / (x difference)
the slope 2/3 tells is that any point
(0 + 3n, 4 + 2n) is on that line.
the ">" in the original inequality tells us that all points with a larger y value than what the line itself would give us are valid. so the whole area up and left of the line is valid.
the line itself has to be dotted or dashed, because ">" also tells us the the points on the line are not included in the set of valid points. otherwise a ">=" has to be used.
and now similar for the other
2x + y <= -5
y <= -2x - 5
turns into
y = -2x - 5
that line goes through
(0, -5) and (0+1, -5 - 2) = (1, -7)
as the slope is -2 = -2/1
and this line is solid, because "<=" was used meaning the points on the line are part of the valid points.
in addition, because of the "<" in "<=" all points with lower y value than the points on the line are valid. so, everything below and left of the line is valid.
the solution to the system of both inequalities is the area, where both areas of valid points overlap.