Question

Which system is represented by the graph?

a. y > 2x
x + 2y ≤ –8

b. y ≥ 2x
x + 2y < –8

c. y < 2x
x + 2y ≥ –8

d. y ≤ 2x
x + 2y > –8

Answer 1

Hi again!

The correct answer is option A

See the graph below

Answer 2

To determine the system of two inequalities which is represented by the graph, you have to do such steps:

1 step. The dashed blue line represents sign > or <. The line has the equation y=2x, then the inequality should be y>2x or y<2x. Since point (-1,1) belongs to the blue shaded region, then the inequallity y>2x is true.

2 step. The solid red line represents sign ≤ or ≥. The line has the equation x+2y=-8, then the inequality should be x+2y≤-8 or x+2y≥-8. Since the origin (0,0) doesn't belong to the red shaded region, then the inequallity x+2y≤-8 is true.

Thus, the system is

`\left\{\begin{array}{l}y>2x\\x+2y\le-8.\end{array}\right.`

Answer: correct choice is A.