Question

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

{y<2/3x
{y≥−x+2

Answer 1

$y < \dfrac{2}{3}x\\\\y=\dfrac{2}{3}x\\\\for\ x=0\to y=\dfrac{2}{3}(0)=0\to(0,\ 0)\\\\for\ x=3\to y=\dfrac{2}{3}(3)=2\to(3,\ 2)\\\\y\geq-x+2\\\\y=-x+2\\\\for\ x=0\to y=-0+2=2\to(0,\ 2)\\\\for\ x=2\to y=-2+2=0\to(2,\ 0)$

$y < \dfrac{2}{3}x$

the dotted line. shadow under the line

$y\geq-x+2$

solid line. shadow above the line

Answer in the attachment (graph C).