Question

Which of the following systems of inequalities represents the graph?

A. y ≤ 2x + 4
y ≥ –x + 2

B. 2x – y ≥ 4
y < –x + 2

C.y ≥ 2x + 4
–x + y ≤ 2

D.–2x + y ≥ 4
x + y < 2

Answer 1

Option D.

Explanation:

Consider the below figure attached with this question.

If a line passes through two points
`(x_1,y_1)` and
`(x_2,y_2)`, then the equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

From the below figure it is clear that the a solid line passes through the points (-2,0) and (0,4). So, the equation of related line is

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

`y=2(x+2)`

`y=2x+4`

`-2x+y=4`

All area above the solid line is shaded. It means the sign of inequality is ≥.

`-2x+y\geq 4`

From the below figure it is clear that the a dashed line passes through the points (2,0) and (0,2). So, the equation of related line is

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

`y=-1(x-2)`

`y=-x+2`

`x+y=2`

All area below the dashed line is shaded. It means the sign of inequality is <.

`x+y<2`

System of inequality is

`-2x+y\geq 4`

`x+y<2`

Therefore, the correct option is D.