Question

Which system of linear inequalities is graphed?

Answer 1

y is greater than or equal to 3x-2

x - 1/2 is less than or equal to 2

Explanation:

the choices aren't shown, but I answered based on the graph.

Answer 2

Option A.

Explanation:

First related equation passes through the points (0,2) and (4,0). So, the equation of line is

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

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

`y-2=-(1)/(2)x`

Multiply both sides by 2.

`2y-4=-x`

`x+2y=4`

The shaded region is below the solid line. So the sign of inequality is ≤.

`x+2y\leq 4` ....(1)

second related equation passes through the points (0,-2) and (2,4). So, the equation of line is

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

`y+2=3x`

`y=3x-2`

The shaded region is above the solid line. So the sign of inequality is ≥.

`y\geq 3x-2` ....(2)

The system of equations contains equation (1) and (2).

Therefore, the correct option is A.