Question

Please Help, Math!!

Which graph represents the solution set of the system of inequalities?

{−2x+y≤4
{y>x+2

Answer 1

The correct answer is the graph in the bottom left. The one below the first graph.





Testing the origin for
$- 2(0) + 0 \leqslant 4$

yields
$0 \leqslant 4$
This is true so we shade the lower half plane
of
$- 2x + y = 4$
Testing the origin for
$y > x + 2$
yields
$0 > 2$

Which is false.

So we shade the upper half plane of
$y = x + 2$
which is the dashed line.

If this are the options:

a . b.
c. d.

Then the graph corresponding to option C is what I am referring to.