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.

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Respuesta :

saralyda04 saralyda04 · Answer 1 · 2019-11-11T23:02:34+01:00

Answer:

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

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erinna erinna · Answer 2 · 2019-12-05T05:59:12+01:00

Answer:

Option B.

Step-by-step explanation:

The given inequalities are

[tex]y<\frac{1}{3}x-1[/tex] .... (1)

[tex]y<\frac{1}{3}x-3[/tex] .... (2)

The related equations of both inequalities are

[tex]y=\frac{1}{3}x-1[/tex]

[tex]y=\frac{1}{3}x-3[/tex]

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).

[tex](0)<\frac{1}{3}(0)-1\Rightarrow 0<-1[/tex] False

[tex](0)<\frac{1}{3}(0)-3\Rightarrow 0<-3[/tex] 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 [tex]y<\frac{1}{3}x-3[/tex] are solutions.

Therefore, the correct option is B.