How do you find the exact solutions to the system #x^2+y^2=25# and #y^2+9x^2=25#?

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Answer 1 · 2018-03-09T14:14:32

See explanation.

The original system is:

#{ (x^2+y^2=25),(y^2+9x^2=25) :}#

From any of the equations you can easily calculate #y^2# in terms of #x^2#:

Now the second equation has only one variable, so we can solve it:

#8x^2=0 => x=0#

Finally we can substitute calculated value of #x#:

#y^2=25-0=>y^2=25 => y=+-5#

Answer: The system has 2 solutions:

#{(x=0),(y=-5):}# and #{(x=0),(y=5):}#