# Can any system be solved using the multiplication method?

##### 1 Answer

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