SOLUTION: Help! I have been trying to figure this problem out and have hit a wall. The problem is regarding non-linear systems. Any help will be greatly appreciated. {(x+1)^2 - (y-1)

Algebra ->  Linear-equations -> SOLUTION: Help! I have been trying to figure this problem out and have hit a wall. The problem is regarding non-linear systems. Any help will be greatly appreciated. {(x+1)^2 - (y-1)      Log On


   

Question 252967: Help! I have been trying to figure this problem out and have hit a wall. The problem is regarding non-linear systems. Any help will be greatly appreciated.
{(x+1)^2 - (y-1)^2 = 20
{ x^2 - (y+2)^2 = 24
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Here is the original question:
(i) %28x%2B1%29%5E2+-+%28y-1%29%5E2+=+20
(ii) +x%5E2+-+%28y%2B2%29%5E2+=+24
Expand (i) and (ii) to see what is going on.
(i) x%5E2+%2B+2x+%2B+1+-y%5E2+%2B+2y++-+1+=+20
(ii) x%5E2+-y%5E2+-+4y+-+4+=+24
subtracting down I get ride of some stuff.
(iii) 2x+%2B+6y+%2B4+=+-4
(iv) 2x+%2B+6y+=+-8
(v) x+=+-3y+-4
Now, we can use substitution back into (ii)
(ii) %28-3y-4%29%5E2+-+%28y%2B2%29%5E2+=+24
8y%5E2%2B+20y++%2B+12+=+24
8Y%5E2+%2B+20y++-12+=+0
By the quadratic, we get
Y = -3 or y = 1/2
If y = -3, then x = 5
If y = 1/2, then x = -11/2.