ax + by + cz = dxyz

>>8801815
Solve it for what? There's one equation and 7 unknowns.

>>8801819

Sorry, solve for sets of x,y,z that satisfy the equation. a,b,c are known constants.

>>8801815
I'm not sure if this is what you're after but you might want to take a look at:
https://en.wikipedia.org/wiki/Diophantine_equation

or do you want to solve the equation explicitly for one particular variable?

>>8801815
[math]x=\frac{by+cz}{dyz-a}[/math]
i think

>>8801815
ax+by+cz=dxyz
by+cz=dxyz-ax
by+cz=x(dyz-a)
x=(by+cz)/(dyz-a)

same kind of factoring can be done for the other variables

>>8801841
>>8801846
Okay I'm not OP but he said that x, y, and z are positive integers. This puts some constraints on the variables. For example, dyz>a, dxz>b, and dxy>c. We also need (by+cz)mod(dyz-a)=(ax+cz)mod(dxz-b)=(ax+by)mod(dxy-c)=0. I don't know how one would satisfy these constraints but I'm just putting it out there.

>>8801846
cant he create a linear system from that method and solve using that?

>>8801863
Calling it a system of equations is kind of misleading. You cannot "create" a system of equations from a single equation. All three equations in your system will be the same thing and it gives no new information.

>>8801867
yeah you're totally right my bad

>>8801853
if the constraints are always true, then the lowest value that xy, xz, and yz can take is 1. That means that d>a, d>b, and d>c.