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