Question

Which system of linear inequalities is represented by the
graph?

Answer 1

y<x+1 y>x-2

Explanation:

upper line: (0,1) (-1,0)

y=x+1

Lower line: (0,-2) (2,0)

y=x-2

I did not see any solid boundry on the line

Shaded: y<x+1 y>x-2

Answer 2

`y <x+1`

`y>x-2`

Explanation:

According to the graph, the system is formed by two inequalities. Let's find out the equation to each line in first place.

Notice that the upper line passes through points (-1,0) and (0,1). First, we find its slope

`m=(y_(2)-y_(1) )/(x_(2)-x_(1) )=(1-0)/(0-(-1))=(1)/(1)=1`

Then, we use the point-slope formula to find the equation

`y-y_(1) =m(x-x_(1) )\\y-0=1(x-(-1)\\y=x+1`

Now, the dashed line indiactes that the inequalities must have sings < or >.

Notice that point (0,0) is part of its solution, that means the inequality is

`y <x+1`

We do the same process to find the other inequality.

The line passes through points (0,-2) and (2,0).

`m=(y_(2)-y_(1) )/(x_(2)-x_(1) )=(0-(-2))/(2-0)=(2)/(2)=1`

Then,

`y-y_(1) =m(x-x_(1) )\\y-0=1(x-2)\\y=x-2`

Notice that point (0,0) is part of its solution, so the inequality is

`y>x-2`

Therefore, the system of inequalities is

`y <x+1`

`y>x-2`