Question

Which point is a solution to the linear inequality y < x 2? (2, 3) (2, 1) (3, –2) (–1, 3)

Answer 1

The linear inequality:
y < x - 2
- 2 < 3 - 2
-2 < 1
Answer:
C )  ( 3, - 2 )

Answer 2

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