Answer: c.(3, 25) and (7, 9)
y = –x^2 + 6x + 16 and y = –4x + 37
Plug in -4x+37 for y in first equation . It becomes
![-x^2 + 6x + 16= -4x+37](https://tex.z-dn.net/?f=%20-x%5E2%20%2B%206x%20%2B%2016%3D%20-4x%2B37%20)
Combine like terms. add 4x and subtract 37 on both sides
![-x^2 + 10x - 21=0](https://tex.z-dn.net/?f=%20-x%5E2%20%2B%2010x%20-%2021%3D0%20)
Divide the whole equation by -1 to remove negative sign from -x^2
![x^2 - 10x + 21=0](https://tex.z-dn.net/?f=%20x%5E2%20-%2010x%20%2B%2021%3D0%20)
Now factor the left hand side
(x-7)(x-3) = 0
x-7 =0 and x-3=0
x= 7 and x=3
Now we find out y using y = –4x + 37
when x= 7 , then y=-4(7) +37 = 9
when x= 3, then y=-4(3) + 37 = 25
We write solution set as (x,y)
(7,9) and (3,25) is our solution set