Question

Which represents the solution(s) of the system of equations, y = –x2 + 6x + 16 and y = –4x + 37? Determine the solution set algebraically.

(3, 25)
(–3, 49)
(3, 25) and (7, 9)
(–3, 49) and (–7, 65)

Answer 1

@dude previously answered this question here:

https://questioncove.com/study#/updates/5aa95846784c457c75773800

Do you just not know how to do that?

Answer 2

the last answer givin didnt answe one of the choices may you give the answer

Answer 3

I'm afraid it isn't our policy that we straight up give out the answer. But I can help you get there. Trust me, this problem isn't that difficult. I'll break it down for you.

Answer 4

\[y = –x^2 + 6x + 16 \]
\[y = –4x + 37\]

Since they are both equal to the same variable, they are both equal to each other. Thus, we can do this:

\[ -4x + 37= -x^2 + 6x + 16 \]
\[x^2 - 10x + 21 = 0\]
\[(x - 3)( x - 7) = 0\]
\[x = 3, 7\]

We need to test both of these variables now.

\[-4(3) + 37 = -(3)^2 + 6(3) + 16\]
\[25 = 25\]

Now lets test 7

\[-4(7) + 37 = (7)^2 + 6(7) + 16\]
\[-28 + 37 = 49 + 42 + 16\]
\[9 = 107\]

This is false. Therefore x = 3, not 7.

Answer 5

Now that we have x, we can solve for y.

\[y = -4x + 37\]
\[y = -4(3) + 37\]
\[y = -12 + 37\]
\[y = 25\]

Answer 6

Let me know if you have any questions regarding the steps

Answer 7

i got it now thanks alot !!!

Answer 8

Oh and this was posted in the Biology section. Moving it to the Mathematics seciton.

Answer 9

No problem @gsmith2002