Question

What is the solution to the following system of equations?
y = -x2 - 5x - 4
y = -x2 + 9x - 18 (2 points)

(-1, -10)
(1, -10)
(-1, 10)
(1, 10)

Answer 1

(-1, 10) is that i got im in a super hurry though i have to go to bed in like 10 mins

Answer 2

what i got*

Answer 3

no i got (1, -10)

Answer 4

Can you show me how i think i did my math wrong

Answer 5

oh wait i think i flipped the negative

Answer 6

so if you plug x = -1 into both equations, do you get y = 10? if so, that's a solution. if not, it isn't.

y = -x^2 - 5x - 4
10 = -(-1)^2 - 5(-1) -4
10 = -1 + 6 - 4
10 = 1
oops. not a solution!

let's try @marigirl's answer

y = -x^2 - 5x - 4
-10 = -(1)^2 - 5(1) - 4
-10 = -1 - 5 - 4
-10 = -10

good so far, but it has to satisfy all the equations in the system

y = -x^2 + 9x - 18
-10 = -(1)^2 + 9(1) - 18
-10 = -1 + 9 - 18
-10 = -10

(1,-10) is the solution to the system of equations.

Answer 7

remember, a common mistake is thinking that -x^2 = (-x)*(-x). it doesn't. it's -1*x*x.

Answer 8

-x^2 - 5x - 4
-x^2 + 9x - 18 - minus one from another
---------------
0x^2 -14x+14
now solve for x

-14x=-14
x=1
then plug in x=1 into any of the original equations. (1, -10)

Answer 9

thank you very much i see my mistake

Answer 10

as for how to solve it, at the solution, obviously y will have the same value for both equations, right?

so we can say

-x^2 - 5x -4 = -x^2 + 9x - 18
add x^2 to both sides
-5x -4 = 9x - 18
add 5x to both sides
-4 = 14x - 18
add 18 to both sides
14 = 14x
x = 1

Answer 11

you can also do it @marigirl's way, but be very careful about the signs when subtracting polynomials. I prefer to multiply one polynomial by -1, then add the two.