Question

Which system of linear inequalities is represented by the graph

Answer 1

The Answer Too Your Question Is C

Answer 2

The correct option is 3.

Explanation:

If a line passing through two points, then the equation of line is

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

Rel line passing through the points (0,-2) and (2,0), then related equation of red line is

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

`y+2=x`

`y=x-2`

Since the shaded region is above the line and the related line is a solid line therefore the sign of inequality must be ≥. The first inequality is

`y\geq x-2`

Blue line passing through the points (0,2) and (4,0), then related equation of red line is

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

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

Multiply 2 on both the sides.

`2y-4=x`

`x+2y=4`

(0,0) is in the shaded region. So, the inequity must be satisfy by (0,0).

`0+2(0)=4`

`0=4`

The related line is dotted, so the required sign of inequality is <. The second inequality is

`x+2y<4`

The system of linear inequalities is defined as

`y\geq x-2`

`x+2y<4`

Therefore the correct option is 3.