Question

Which system is equivalent to 3x squared - 4y squared = 25 over -6x squared -2y squared = 11

Answer 1

So we are given the following system:
$3x^2-4y^2=25\\ -6x^2-2y^2=11\\\text{Multiply the second equation by -2:}\\12x^2+4y^2=-22\\\text{Add to the first equation we get:}\\15x^2=3 \text{ therefore }x=\pm \sqrt{ \frac{1}{5} }$
Using the first equation again we get:
$3x^2-4y^2=25\\ 3x^2=4y^2+25\\ x^2= \frac{1}{3}(4y^2+25)\\x^2= \frac{1}{3}(4 \frac{1}{5} +25)\\= \frac{43}{5}\\x=\pm \sqrt{ \frac{43}{5} }$