Can somebody explain how my solutions manual got the shaded area in their graph ( attached), for the below system? 2x - y 4 y

Question

Can somebody explain how my solutions manual got the shaded area in their graph ( attached), for the below system?
2x - y > 4
y < -(x*x) + 2
I'm having problems understanding, how to figure out where to shade from a given system..

anonymous · Answer

reorganising: y < 2x - 4 is the region BELOW the line y = 2x - 4.

y<-x^2 + 2 is an upside down parabola. This region is is all of inside the parabola.

The overall region is the common part of these two regions: below the line AND inside the parabola.

does this make sense?

anonymous · Answer

I'm not in modern algebra..therefor your superscript upside down 'v' is confusing as to exactly what it means to me..

anonymous · Answer

Oooh, I was right! Can you see the dotted region under the line y=2x-4? The curve y=-x^2 +2 is what I called an 'upside down' parabola (if it were y=+x^2 + 2, it would be pointing upwards). This type of curve is a parabola.

The shaded region below this curve is all 'inside' the curve.

The region you are looking for is the OVERLAP of the two regions (shaded dark in your diagram).

hth