Question

The inequality x + 2y ≥ 3 is satisfied by which of the following points? (Select all that apply.)

(1, 1)
(-3, 4)
(-2, 2)
(5, -2)

Answer 1

For this case we have the following inequality:

`x + 2y \geq3`

We substitute each of the points and see which one is fulfilled:

Point A: (1,1)

`1 + 2 (1) \geq3\\1 + 2 \geq3\\3 \geq3`

Is fulfilled!

Point B: (-3,4)

`-3 + 2 (4) \geq3\\-3 + 8 \geq3\\5 \geq3`

Is fulfilled!

Point C: (-2,2)

`-2 + 2 (2) \geq3\\-2 + 4 \geq3\\2 \geq3`

It is not fulfilled!

Point D: (5, -2)

`5 + 2 (-2) \geq3\\5-4 \geq3\\1 \geq3`

It is not fulfilled!

Answer:

Option A and B

Answer 2

(1,1), (-3,4)

Explanation:

Given x + 2y ≥ 3

Rewrite the inequality as;

x + 2y = 3

Form a table for values of x and y

x y

3 0

1 1

-3 3

Plot the points on a Cartesian plane

From the graph, the points are; (1,1), (-3,4)