Q:

Find the solution of system of non linear equations

The system of equations:

$x+2x^2+3xy+0y=6$
$2x+x^2+3xy+y=5$
$x-1x^2+0xy+y=7$

options are

has solutions in rational nos
has solutions in real nos
has no solution
has solutions in complex nos

Actually, I know to system of linear equations solving methods but I don't have any idea about to solve this kind  system of equations. 
I guess the system of equations has solution is complex nos.   But I am not sure the answer. 

A:

$$i)x+2x^2+3xy=6\\ii)2x+x^2+3xy+y=5\\iii)x-x^2+y=7$$
We add $i)$ and $iii)$ to obtain $$x+2x^2+3xy+x-x^2+y=2x+x^2+3xy+y=13$$
But $ii)$ tells us that $2x+x^2+3xy+y=5$
Both cannot hold so the system has no solution.