Question 1062395: I am trying to figure how to find part of answer to this non-linear system:
(X+1)^2 - (y-1)^2 = 20
X^2 - (y+2)^2 = 24
I used elimination to end up with the answers of y = 1/2 and x = -11/2.
This has been confirmed via graphing. Problem is there is another common point of 5,-3, but I cannot figure out how to come do it algebraically. Any help would be appreciated. Thank you!
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website! .
(x+1)^2 - (y-1)^2 = 20
x^2 - (y+2)^2 = 24
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(x+1)^2 - (y-1)^2 = 20, (1)
X^2 - (y+2)^2 = 24. (2)
Open parentheses:
x^2 + 2x + 1 - y^2 + 2y - 1 = 20, (3)
x^2 - y^2 - 4y - 4 = 24. (4)
Distract (4) from (3) (both sides). You will get
2x + 1 + 6y + 3 = -4, or
2x + 6y = -8, or
x + 3y = -4. (5)
Express x = -3y - 4 from (5) and substitute it into (2), replacing x. You will get
(-3y - 4)^2 - (y+2)^2 = 24, or
9y^2 + 24y + 16 - y^2 - 4y - 4 = 24, or
8y^2 + 20y - 12 = 0, or
2y^2 + 5y - 3 = 0.
 =  =  .
The roots are  =  ,  = -3.
For each root find the corresponding value of x.
Can you complete it on your own?
If you want to see more similar solved problems, look into the lesson
- Solving systems of algebraic equations of degree 2
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Systems of equations that are not linear".
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