Question

3x−4y>12

Which ordered pair (x, y) satisfies the inequality?

(0,0)


(−5,−4)


(0,−4)


(4,0)

Answer 1

we test each of them

`3 * 0 - 4 * 0 > 12`

it's false so (0,0) is not the answer

`3 * ( - 5) - 4 * ( - 4) = 1 > 12`

this is also false so (-5,-4) isn't the answer

`3 * 0 - 4 * ( - 4) = 16 > 12`

this is true so this is the answer

`3 * 4 - 4 * 0 > 12`

this is false so it's not the answer

Answer 2

(c) (0,−4)

Explanation:

An ordered pair satisfies the inequality if it is found inside the solution space on the graph of the inequality.

__

graph

The boundary line equation is in standard form, so the x- and y-intercepts are easily found.

x-intercept: for y=0, we have 3x = 12 ⇒ x = 12/3 = 4

y-intercept: for x=0, we have -4y = 12 ⇒ y = 12/-4 = -3

The inequality does not include the "or equal to" case, so the boundary line is dashed. Shading is to the right (x>) or below (y<) the line.

__

solution

The only ambiguous point is the one at (4, 0) that is on the boundary line. Since the boundary line is dashed, it is not part of the solution set. (4, 0) does not satisfy the inequality. (it makes the inequality be 12>12, which is false)

Here, the graph shows the only ordered pair listed that satisfies the inequality is (0, -4).