Question

Which ordered pairs are in the solution set of the system of linear inequalities? y > -1/2x y <1/2 x + 1

Answer 1

Look at the picture.

$y=-\dfrac{1}{2}x\\\\for\ x=0\to y=-\dfrac{1}{2}\cdot0=0\to(0;\ 0)\\\\for\ x=2\to y=-\dfrac{1}{2}\cdot2=-1\to(2;\ -1)\\\\\\y=\dfrac{1}{2}x+1\\\\for\ x=-2\to y=\dfrac{1}{2}\cdot(-2)+1=-1+1=0\to(-2;\ 0)\\\\for\ x=0\to y=\dfrac{1}{2}\cdot0+1=1\to(0;\ 1)$

Answer: Every points on orange area.