Solve the systems of equations in real numbers $a$,$b$,$c$,$d$

Question

Solve the simultaneus equations

$ab$ + $c$ + $d$ = $3$

$bc$ + $d$ + $a$ = $5$

$cd$ + $a$ + $b$ = $2$

$da$ + $b$ + $c$ = $6$, where $a$,$b$,$c$,$d$ are real numbers.

I tried to add all of them and factor them as $xy$ + $x$ + $y$ = $(x+1)(y+1)$ - $1$. Thank you for your responses.

Answer 1

Assuming the last was supposed to be $da+b+c=6$ from the symmetry of the variables, Alpha finds $a=2, b=c=0, d=3$ which is easy to verify. It can also solve the problem as written, but the solutions are not as clean.

Answer 2

Using Maple's Groebner basis package, there is a unique solution in complex numbers -- namely $(a,b,c,d) = (2,0,0,3)$, as previously noted by Ross Millikan.