Question

Which represents the solution(s) of the system of equations, y = –x2 + 6x + 16 and y = –4x + 37? Determine the solution set algebraically.
a.(3, 25)
b.(–3, 49)
c.(3, 25) and (7, 9)
d.(–3, 49) and (–7, 65)

Answer 1

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

$-x^2 + 6x + 16= -4x+37$

Combine like terms. add 4x  and subtract 37 on both sides

$-x^2 + 10x - 21=0$

Divide the whole equation by -1 to remove negative sign from -x^2

$x^2 - 10x + 21=0$

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

Answer 2

TO determine the solution set of the equations given above, we can use substitution method. We do as follows:

y = –x2 + 6x + 16 and y = –4x + 37

 –x2 + 6x + 16  = –4x + 37
-x^2 +10x -21 = 0
x = 7 and 3
y = 9 and 25

Therefore, option C is the correct answer.