SOLUTION: Solve the system: x^2+y^2=63 x^2-3y^2=27 (A) (3 sqrt 6, 3) (3 sqrt 6, -3) (-3 sqrt 6, 3) (-3 sqrt6, -3) (B) (-3 sqrt6, 3) ( -3 sqrt6, -3) (C) 3 sqrt6, 3) (3 sqrt 6, -3) (D)

Question 30460: Solve the system:
x^2+y^2=63
x^2-3y^2=27
(A) (3 sqrt 6, 3) (3 sqrt 6, -3) (-3 sqrt 6, 3) (-3 sqrt6, -3)
(B) (-3 sqrt6, 3) ( -3 sqrt6, -3)
(C) 3 sqrt6, 3) (3 sqrt 6, -3)
(D) 1, sqrt 62) (1, -swrt 62) (-1, sqrt 62) (-1, -sqrt 62)
Please be specific as to which letter answer is correct.
Thanks
Answer by mukhopadhyay(490) (Show Source): You can put this solution on YOUR website!
x^2+y^2=63
=> x^2=63-y^2
By substituting x^2 in the second equation:
x^2-3y^2=27
=>(63-y^2)-3y^2=27
=>-y^2-3y^2 = 27-63
=> -4y^2 = -36
=> y^2 = 9
=> y = 3 or y = -3
x^2 = 63-y^2
=>x^2 = 63-9
=>x^2 = 54
=>x = sqrt(54) or x = -sqrt(54)
=>x = 3sqrt(6) or x = -3sqrt(6)
Answer: x = 3 or -3; y = 3sqrt(6) or y = -3sqrt(6)

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