I have many equations of this form:
$cf+ce-bg-ag=j$
$af+ch-dg-be=l$
$cj=j$
$aj+cl=l$
$cm+cn-ao-bo=n$
$an+cp-do-bm=p$
$gj=n$
$ej+gl=p$
I would like to make a computer program to solve systems of this form, so I need a general algorithm, and not some heuristics. If it helps, the summands on the left side of the equations will always be a product of at most two variables, and the summands on the right hand side will always be a product of at most one variable.