## anonymous 5 years ago 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.

1. anonymous

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.

2. anonymous

ok I'll try that

3. anonymous

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

4. anonymous

"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.

5. anonymous

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

6. anonymous

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

7. anonymous

Yes

8. anonymous

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.

9. anonymous

okay thank you so much!

10. anonymous

y=3 & y=-3