SOLUTION: x^2+y^2=9 x^2+6y^2=36

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Question 540551: x^2+y^2=9
x^2+6y^2=36
Answer by Maths68(1474) About Me  (Show Source):
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x%5E2%2B6y%5E2=36............(1)
x%5E2%2By%5E2=9..............(2)
Subtract (2) from (1)
x%5E2%2B6y%5E2=36
-x%5E2-y%5E2=-9
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5y%5E2=27
Divide by 5 both sides
5y%5E2%2F5=27%2F5
cross%285%29y%5E2%2Fcross%285%29=27%2F5
y%5E2=27%2F5
Take square root both sides
sqrt%28y%5E2%29=sqrt%2827%2F5%29
y=sqrt%2827%2F5%29
Put the value of y in (2)
x%5E2%2By%5E2=9..............(2)
x%5E2%2B%28sqrt%2827%2F5%29%29%5E2=9
x%5E2%2B%2827%2F5%29=9
x%5E2=9-%2827%2F5%29
x%5E2=%2845-27%29%2F5
x%5E2=18%2F5
Take square root both sides
sqrt%28x%5E2%29=sqrt%2818%2F5%29
x=sqrt%2818%2F5%29


Check
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Put the values of x and y in (2)
x%5E2%2By%5E2=9..............(2)
%28sqrt%2818%2F5%29%29%5E2%2B%28sqrt%2827%2F5%29%29%5E2=9
%2818%2F5%29%2B%2827%2F5%29=9
%2818%2B27%29%2F5%29=9
%2845%2F5%29=9
9=9

Put the values of x and y in (1)
x%5E2%2B6y%5E2=36............(1)
%28sqrt%2818%2F5%29%29%5E2%2B6%28%28sqrt%2827%2F5%29%29%5E2%29=36
18%2F5%2B%286%2827%2F5%29%29=36
18%2F5%2B%28162%2F5%29%29=36
%2818%2B162%29%2F5=36
180%2F5=36
36=36