Which ordered pair is a solution to the system of inequalities? y > –x
y ≤ x + 1

A) (0,5)

B) (4,–1)

C) (1,3)

D) (–4,0)

9514 1404 393

  B) (4,–1)

Step-by-step explanation:

A graph can help you figure this out. The point (4, -1) is in the doubly-shaded area, so is a solution to this system.

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Explanation:

Choice A can be ruled out because

which is false.

Choices C and D are similar, so they can be ruled out as well.

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Choice B is the answer because it makes both inequalities true.

If we plug the coordinates of (4,-1) into the first inequality, we get

which is a true statement because -1 is to the right of -4 on the number line.

Now try the other inequality

that's true also. So again, (4,-1) makes both inequalities true, and that's why choice B is the answer.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3