Question 30340: Solve the system:
x^2+y^2=63
x^2=3y^2=27
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! Solve the system:
x^2+y^2=63
x^2=3y^2=27
If the problem is
x^2+y^2=63 ----(1)
x^2-3y^2=27 ----(2)
(1) - (2)
(x^2-x^2)+[y^2-(-3y^2)]= 63-27
0 + (y^2+3y^2) = 36
4y^2 = 36
y^2 = 36/4 = 9 ----(*)
y = +3 or y = -3
y^2 = 9 in (1) gives
x^2+y^2 = 63
x^2+9 = 63
x^2 = 63-9
x^2=54 ----(**)
x= +[sqrt(54)] and x = -[sqrt(54)]
Answer:(sqrt(54),3), (sqrt(54),-3), (-sqrt(54),3),(-sqrt(54),-3)
That is (3sqrt(6),3),(3sqrt(6),-3),(-3sqrt(6),3),(-3sqrt(6),-3),
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