Question

Which is true about the solution to the system of inequalities shown?

y < One-thirdx – 1

y < One-thirdx – 3

On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (0, negative 1) and (2, 0). Everything below the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (3, negative 2). Everything below the line is shaded.
All values that satisfy y < One-thirdx – 1 are solutions.
All values that satisfy y < One-thirdx – 3 are solutions.
All values that satisfy either y < One-thirdx – 1 or y < One-thirdx – 3 are solutions.
There are no solutions.

Answer 1

B. All values that satisfy y < 1/3x – 3 are solutions.

Answer 2

Option B.

Explanation:

The given inequalities are

`y<(1)/(3)x-1` .... (1)

`y<(1)/(3)x-3` .... (2)

The related equations of both inequalities are

`y=(1)/(3)x-1`

`y=(1)/(3)x-3`

Table of values:

For inequality (1).

x y

0 -1

3 0

For inequality (2).

x y

0 -3

9 0

Plot these points on a coordinate plane and draw both related lines.

Check the inequalities by (0,0).

`(0)<(1)/(3)(0)-1\Rightarrow 0<-1` False

`(0)<(1)/(3)(0)-3\Rightarrow 0<-3` False

It means (0,0) is not included in shaded area of any inequality.

From the given graph it is clear that all values that satisfy
`y<(1)/(3)x-3` are solutions.

Therefore, the correct option is B.