Question

Which ordered pairs are solutions to the inequality 2x+y>−4?

Answer 1

Sub in ur answer choices to see which ones work

solutions are : (5,-12) , (-3,0), (-1,1), (0,1)...only one that doesn't work is (4,-12)...and that is only because the problem does not contain an equal sign

Answer 2

we will proceed to resolve each case to determine the solution

we have

$2x+y>-4$

$y>-2x-4$

we know that

If an ordered pair is the solution of the inequality, then it must satisfy the inequality.

case a) $(5,-12)$

Substitute the value of x and y in the inequality

$-12>-2*5-4$

$-12>-14$ ------> is True

therefore

the ordered pair $(5,-12)$ is a solution of the inequality

case b) $(-3,0)$

Substitute the value of x and y in the inequality

$0>-2*-3-4$

$0>2$ ------> is False

therefore

the ordered pair $(-3,0)$ is not a solution of the inequality

case c) $(-1,-1)$

Substitute the value of x and y in the inequality

$-1>-2*-1-4$

$-1>-2$ ------> is True

therefore

the ordered pair$(-1,-1)$ is a solution of the inequality

case d) $(0,1)$

Substitute the value of x and y in the inequality

$1>-2*0-4$

$1>-4$ ------> is True

therefore

the ordered pair $(0,1)$ is a solution of the inequality

case e) $(4,-12)$

Substitute the value of x and y in the inequality

$-12>-2*4-4$

$-12>-12$ ------> is False

therefore

the ordered pair $(4,-12)$ is not a solution of the inequality

Verify

using a graphing tool

see the attached figure

the solution is the shaded  area above the line

The points A,C, and D lies on the shaded area, therefore the ordered pairs A,C, and D are solution of the inequality