Question

Determine whether (2,-1) and (-4,2) satisfy the inequality 2x-3y>4. Neither (2,-1) nor (-4,2) satisfies the inequality. (-4,2) satisfies the inequality, but (2,-1) does not. (2,-1) satisfies the inequality, but (-4,2) does not. Both (2,-1) and (-4,2) satisfy the inequality.

Answer 1

(2,-1) satisfies the inequality, but (-4,2) does not.

Explanation:

To verify if the points satisfy the inequality, we replace then in the inequality, and see if we have a true statement or a false one.

(2,-1)

`x = 2, y = -1`

So

`2x - 3y > 4`

`2(2) - 3(-1) > 4`

`4 + 3 > 7`

`7 > 4`

This is a true statement, which means that (2,-1) satisfies the inequality.

(-4,2)

`x = -4, y = 2`

So

`2x - 3y > 4`

`2(-4) - 3(2) > 4`

`-8 - 6 > 7`

`-14 > 4`

This is a false statement, so (-4,2) does not satisfy the inequality.

The correct answer is:

(2,-1) satisfies the inequality, but (-4,2) does not.