Can any system be solved using the multiplication method?
I assume that you are only asking about linear systems.
I also need to assume that, like me, you count discovering that a system has no solutions (is inconsistent) counts as "solving the system"
Third, I assume that the number of variables equals the number of equations.
Finally, I assume that the "multiplication method" is the same as the method I was taught to call the "addition/subtraction method".
With these four assumptions, the answer is,
Yes. Any linear system of
Mutiply the first equation by
Add to get:
So, as long as we don't have
Using the number we get for