Alternative ![1](https://tex.z-dn.net/?f=1)
we have
![y < x+2](https://tex.z-dn.net/?f=y%20%3C%20x%2B2)
we know that
If a point is a solution of the inequality
then
the point must be satisfy the inequality
we're going to verify all the points.
<u>case A)</u> point ![(2,3)](https://tex.z-dn.net/?f=%282%2C3%29)
Substitute the value of x and the value of y in the inequality
![x=2\ y=3](https://tex.z-dn.net/?f=x%3D2%5C%20y%3D3)
![y < x+2](https://tex.z-dn.net/?f=y%20%3C%20x%2B2)
![3 < 2+2](https://tex.z-dn.net/?f=3%20%3C%202%2B2)
------> is true
therefore
The point
is a solution of the inequality
<u>case B)</u> point ![(2,1)](https://tex.z-dn.net/?f=%282%2C1%29)
Substitute the value of x and the value of y in the inequality
![x=2\ y=1](https://tex.z-dn.net/?f=x%3D2%5C%20y%3D1)
![y < x+2](https://tex.z-dn.net/?f=y%20%3C%20x%2B2)
![1< 2+2](https://tex.z-dn.net/?f=1%3C%202%2B2)
------> is true
therefore
The point
is a solution of the inequality
<u>case C)</u> point ![(3,-2)](https://tex.z-dn.net/?f=%283%2C-2%29)
Substitute the value of x and the value of y in the inequality
![x=3\ y=-2](https://tex.z-dn.net/?f=x%3D3%5C%20y%3D-2)
![y < x+2](https://tex.z-dn.net/?f=y%20%3C%20x%2B2)
![-2< 3+2](https://tex.z-dn.net/?f=-2%3C%203%2B2)
------> is true
therefore
The point
is a solution of the inequality
<u>case D)</u> point ![(-1,3)](https://tex.z-dn.net/?f=%28-1%2C3%29)
Substitute the value of x and the value of y in the inequality
![x=3\ y=-2](https://tex.z-dn.net/?f=x%3D3%5C%20y%3D-2)
![y < x+2](https://tex.z-dn.net/?f=y%20%3C%20x%2B2)
![3< -1+2](https://tex.z-dn.net/?f=3%3C%20-1%2B2)
------> is not true
therefore
The point
is not a solution of the inequality
Alternative ![2](https://tex.z-dn.net/?f=2)
we have
![y < x-2](https://tex.z-dn.net/?f=y%20%3C%20x-2)
we know that
If a point is a solution of the inequality
then
the point must be satisfy the inequality
we're going to verify all the points.
<u>case A)</u> point ![(2,3)](https://tex.z-dn.net/?f=%282%2C3%29)
Substitute the value of x and the value of y in the inequality
![x=2\ y=3](https://tex.z-dn.net/?f=x%3D2%5C%20y%3D3)
![y < x-2](https://tex.z-dn.net/?f=y%20%3C%20x-2)
![3 < 2-2](https://tex.z-dn.net/?f=3%20%3C%202-2)
------> is not true
therefore
The point
is not a solution of the inequality
<u>case B)</u> point ![(2,1)](https://tex.z-dn.net/?f=%282%2C1%29)
Substitute the value of x and the value of y in the inequality
![x=2\ y=1](https://tex.z-dn.net/?f=x%3D2%5C%20y%3D1)
![y < x-2](https://tex.z-dn.net/?f=y%20%3C%20x-2)
![1< 2-2](https://tex.z-dn.net/?f=1%3C%202-2)
------> is not true
therefore
The point
is not a solution of the inequality
<u>case C)</u> point ![(3,-2)](https://tex.z-dn.net/?f=%283%2C-2%29)
Substitute the value of x and the value of y in the inequality
![x=3\ y=-2](https://tex.z-dn.net/?f=x%3D3%5C%20y%3D-2)
![y < x-2](https://tex.z-dn.net/?f=y%20%3C%20x-2)
![-2< 3-2](https://tex.z-dn.net/?f=-2%3C%203-2)
------> is true
therefore
The point
is a solution of the inequality
<u>case D)</u> point ![(-1,3)](https://tex.z-dn.net/?f=%28-1%2C3%29)
Substitute the value of x and the value of y in the inequality
![x=3\ y=-2](https://tex.z-dn.net/?f=x%3D3%5C%20y%3D-2)
![y < x-2](https://tex.z-dn.net/?f=y%20%3C%20x-2)
![3< -1-2](https://tex.z-dn.net/?f=3%3C%20-1-2)
------> is not true
therefore
The point
is not a solution of the inequality