Question

Which system of inequalities is represented by the graph?

Answer 1

C.
`y<-(x)/(2)` and
`y\geq -1`

Explanation:

We know that,

Zero Test states that 'After substituting the point (0,0) in the inequalities, if the result is true, the solution region is towards the origin. If the result is false, the solution region is away from the origin'.

So, from the graph, we see that,

The solution region of line y= -1 is towards the origin and so, the result after substitution of (0,0) must be true.

Also, the line y= -1 is in bold i.e. there will be equal sign in the equality.

Thus, the corresponding true inequality will be
`y\geq -1`

Similarly, we see that,

The solution region of the other straight line is towards the origin and so, the result after substitution of (0,0) must be true.

Also, the other line is in dotted i.e. there will be no equal sign in the equality.

Thus, the corresponding true inequality will be
`y<-(x)/(2)`

Hence, option C is correct.

Answer 2

Option 3 is the correct answer.

Explanation:

In this graph the red area is above the line y = -1 which represents y ≥ (-1)

Another graph is of a line y = mx + c which passes through (2, -1) and (0, 0)

where m = (y-y')/(x-x') = (1+0)/(0-2) = -1/2

and y intercept c = 0

Therefore line is y = -1/2x

and the blue area will be y ≤ -1/2x below the line.

Hence Option 3 is the answer.