Question

Which system of linear inequalities is represented by the graph?

Answer 1

The answer for this is B.

Answer 2

The system of linear inequalities is represented by the graph is:

`y>(2)/(3)x+3\ ,\ y\leq -(1)/(3)x+2`

Explanation:

Clearly from the graph we could observe that as one of the inequality is a strict inequality while the other is a inequality with a equality sign.

Since, one of line is dotted and the other is a solid line.

Also, we see that:

• The dotted line is a line passing through (-3,1) and (0,3)

Hence, the equation of line is:

`y-1=(3-1)/(0-(-3))* (x-(-3))\\\\\\y-1=(2)/(3)* (x+3)\\\\\\y=(2)/(3)x+2+1\\\\\\y=(2)/(3)x+3`

and also we could see that the shaded region is away from the origin.

Hence, the inequality is:

`y>(2)/(3)x+3`

• Similarly the other equation is a solid line passing through (6,0) and (0,2)

Hence, the equation of this line is:

`y-0=(2-0)/(0-6)* (x-6)\\\\\\y=(2)/(-6)* (x-6)\\\\\\y=-(1)/(3)x+2`

Also, the shaded region is towards the origin.

Hence, the inequality that holds true is:

`y\leq -(1)/(3)x+2`