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.