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

Option B.

Explanation:

The given inequalities are

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

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

The related equations of given inequalities are

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

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

The tables of values are

For line 1 For line 2

x y x y

0 -1 0 -3

3 0 9 0

Plot these ordered pairs on a coordinate plane and connect them by straight lines.

The sign of both inequalities is "<" it means both lines are dotted and everything below the lines is shaded.

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

Therefore, the correct option is B.