Question

This is my last problem on this sample work. Dx Please help! There are no multiple choice options so this is a free for all. Thank you!!

Answer 1

`\left\{\begin{array}{l}y\ge 2x+4\\ \\y<-x+2\end{array}\right.`

Explanation:

1. The solid line passes trough the points (0,4) and (-2,0). The equation of this line is:

`(x-0)/(-2-0)=(y-4)/(0-4)\\ \\y-4=2x\\ \\y=2x+4`

The origin doesn't belong to the shaded region, so its coordinates do not satisfy the inequality. Thus,

`y\ge 2x+4`

2. The dotted line passes trough the points (0,2) and (2,0). The equation of this line is:

`(x-0)/(2-0)=(y-2)/(0-2)\\ \\y-2=-x\\ \\y=-x+2`

The origin belongs to the shaded region, so its coordinates satisfy the inequality. Thus,

`y< -x+2`

Hence, the system of two inequalities is