SOLUTION: x^2+y^2=11 2x^2-y^2=-2

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Question 147119: x^2+y^2=11
2x^2-y^2=-2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2By%5E2=11 Start with the first equation.


y%5E2=11-x%5E2 Solve for y%5E2


2x%5E2-y%5E2=-2 Move onto the second equation.


2x%5E2-%2811-x%5E2%29=-2 Plug in y%5E2=11-x%5E2


2x%5E2-11%2Bx%5E2=-2 Distribute


-11%2B3x%5E2=-2 Combine like terms on the left side.


3x%5E2=-2%2B11 Add 11 to both sides.


3x%5E2=9 Combine like terms on the right side.


x%5E2=%289%29%2F%283%29 Divide both sides by 3 to isolate x%5E2.


x%5E2=3 Reduce. Make a special note of this since we'll use this later.


x+=+0+%2B-+sqrt%283%29 Take the square root of both sides.


x+=+sqrt%283%29 or x+=+-sqrt%283%29 Break up the expression



So our x answers are x+=+sqrt%283%29 or x+=+-sqrt%283%29


y%5E2=11-x%5E2 Go back to the first isolated equation


y%5E2=11-3 Plug in x%5E2=3


y%5E2=8 Combine like terms.


y+=+0+%2B-+sqrt%288%29 Take the square root of both sides.


y+=+sqrt%288%29 or y+=+-sqrt%288%29 Break up the expression.


y+=+2%2Asqrt%282%29 or y+=+-2%2Asqrt%282%29 Simplify



So our y answers are y+=+2%2Asqrt%282%29 or y+=+-2%2Asqrt%282%29



So the solutions are , , , and