Alternative [tex]1[/tex]
we have
[tex]y < x+2[/tex]
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.
case A) point [tex](2,3)[/tex]
Substitute the value of x and the value of y in the inequality
[tex]x=2\ y=3[/tex]
[tex]y < x+2[/tex]
[tex]3 < 2+2[/tex]
[tex]3 < 4[/tex] ------> is true
therefore
The point [tex](2,3)[/tex] is a solution of the inequality
case B) point [tex](2,1)[/tex]
Substitute the value of x and the value of y in the inequality
[tex]x=2\ y=1[/tex]
[tex]y < x+2[/tex]
[tex]1< 2+2[/tex]
[tex]1 < 4[/tex] ------> is true
therefore
The point [tex](2,1)[/tex] is a solution of the inequality
case C) point [tex](3,-2)[/tex]
Substitute the value of x and the value of y in the inequality
[tex]x=3\ y=-2[/tex]
[tex]y < x+2[/tex]
[tex]-2< 3+2[/tex]
[tex]-2 < 5[/tex] ------> is true
therefore
The point [tex](3,-2)[/tex] is a solution of the inequality
case D) point [tex](-1,3)[/tex]
Substitute the value of x and the value of y in the inequality
[tex]x=3\ y=-2[/tex]
[tex]y < x+2[/tex]
[tex]3< -1+2[/tex]
[tex]3 < 1[/tex] ------> is not true
therefore
The point[tex](-1,3)[/tex] is not a solution of the inequality
Alternative [tex]2[/tex]
we have
[tex]y < x-2[/tex]
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.
case A) point [tex](2,3)[/tex]
Substitute the value of x and the value of y in the inequality
[tex]x=2\ y=3[/tex]
[tex]y < x-2[/tex]
[tex]3 < 2-2[/tex]
[tex]3 < 0[/tex] ------> is not true
therefore
The point [tex](2,3)[/tex] is not a solution of the inequality
case B) point [tex](2,1)[/tex]
Substitute the value of x and the value of y in the inequality
[tex]x=2\ y=1[/tex]
[tex]y < x-2[/tex]
[tex]1< 2-2[/tex]
[tex]1 < 0[/tex] ------> is not true
therefore
The point [tex](2,1)[/tex] is not a solution of the inequality
case C) point [tex](3,-2)[/tex]
Substitute the value of x and the value of y in the inequality
[tex]x=3\ y=-2[/tex]
[tex]y < x-2[/tex]
[tex]-2< 3-2[/tex]
[tex]-2 < 1[/tex] ------> is true
therefore
The point [tex](3,-2)[/tex] is a solution of the inequality
case D) point [tex](-1,3)[/tex]
Substitute the value of x and the value of y in the inequality
[tex]x=3\ y=-2[/tex]
[tex]y < x-2[/tex]
[tex]3< -1-2[/tex]
[tex]3 < -3[/tex] ------> is not true
therefore
The point [tex](-1,3)[/tex] is not a solution of the inequality
