Question

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

{y<2/3x
{y≥−x+2

Answer 1

`y < (2)/(3)x\\\\y=(2)/(3)x\\\\for\ x=0\to y=(2)/(3)(0)=0\to(0,\ 0)\\\\for\ x=3\to y=(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 < (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).