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 ${(x=0),(y=5):}$