Question

solve....x. and y

$47x + 31y = 63 \\ 31x + 47y = 15$

Answer 1

47/31=31/47is not=-63/-15
no solution

Answer 2

Multiply equation 1 by 31 and equation 2 by 47.

So elements of x are nullified...

i.e. (2) - (1)

${47}^{2} y - {31}^{2} y = 47 \times 15 - 63 \times 31$
=> $(47 + 31)(47 - 31)y = 705 - 1953$
=> $(78)(16)y = - 1248$
=> $y = - 1$
as 1248=78*16,..

So,
$x = \frac{63 - 31y}{47}$
=> $x = 2$
So the pair is (2,-1)...

And btw my gaming name is maverick... ;)