Question

Which system of linear inequalities is represented by the graph?

y > x + 3 and 3x – y > 2
y > x + 3 and 3x – y > 2
y > x + 3 and 3x + y > 2
y > x + 3 and 2x – y > 2

Answer 1

Im not good in math and this is my first question, my best guess is D

I will investigate tommorow this problem a little bit more... <3

Answer 2

The graph represent the system of linear inequalities
`y>(1)/(3)(x)+3` and
`3x-y>2`.

Explanation:

From the given given graph it is clear that the red line passing through the point (0,3) and (-3,2). The black line passing through the points (0,-2) and (1,1).

If a line passing through two points, then the equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

The related equation of red line is

`y-3=(2-3)/(-3)(x-0)`

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

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

The red line is dotted and shaded potion is upper side of the line, therefore the sign of inequality is >.

`y>(1)/(3)(x)+3` .... (1)

The related equation of black line is

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

`y+2=3x`

The black line is dotted and shaded potion is lower side of the line, therefore the sign of inequality is <.

`y+2<3x`

`2<3x-y`

`3x-y>2` .... (2)

Therefore the graph represent the system of linear inequalities
`y>(1)/(3)(x)+3` and
`3x-y>2`.