Question

I would really appreciate it if someone could help me with this problem thanks
x^2=2y^2-2x+8y+5
x^2=26y^2-2x+104y+77
Solve the following systems of equations
Answer must be in simplest form.

Answer 1

You can put both in the form:
\[x^2 + 2x = f(y) \text{ and } g(y) \implies f(y) = g(y) \]

Solve this for y (you can cancel a LOT before you start) and put it back in for x.

Answer 2

ok I'll try that

Answer 3

okay so I decided to use the elimination method I put everything with variable on one side and the number on the other side for both equations.
Then I multiplied one equation by -1
I was left with 24y^2+112y=72
Then i divided everything by 8 I got 3y^2+14y=9
I moved the 9 over so it becomes neg & the equationis = to zero
Now I am stuck on what to do can you help with the next step? Thanks

Answer 4

"I was left with 24y^2+112y=72"

You shouldn't have been. You should have (104-8)y not (104+8)y.

The former cancels much more nicely with the y^2 and constant term.

Answer 5

oh okay I see what i did i forgot the neg sign. Thank you! I will try again

Answer 6

so it should by 96y instead of 112y right?

Answer 7

Yes

Answer 8

Sorry, I have to go, but hopefully you will see the (big) factor that cancels and you can solve it easily got the two y values, then plug back in for x.

Answer 9

okay thank you so much!

Answer 10

y=3 & y=-3