Answer :
Answer:
y<x+1 y>x-2
Step-by-step 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:
[tex]y <x+1[/tex]
[tex]y>x-2[/tex]
Step-by-step 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
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }=\frac{1-0}{0-(-1)}=\frac{1}{1}=1[/tex]
Then, we use the point-slope formula to find the equation
[tex]y-y_{1} =m(x-x_{1} )\\y-0=1(x-(-1)\\y=x+1[/tex]
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
[tex]y <x+1[/tex]
We do the same process to find the other inequality.
The line passes through points (0,-2) and (2,0).
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }=\frac{0-(-2)}{2-0}=\frac{2}{2}=1[/tex]
Then,
[tex]y-y_{1} =m(x-x_{1} )\\y-0=1(x-2)\\y=x-2[/tex]
Notice that point (0,0) is part of its solution, so the inequality is
[tex]y>x-2[/tex]
Therefore, the system of inequalities is
[tex]y <x+1[/tex]
[tex]y>x-2[/tex]