# Solving linear equations involving many variables

I know that to solve a linear equation involving $$n$$ variables for example, we need $$n-1$$ other independent equations to form a system and then solve that system. Is there a formal proof for this?

• It depends on the type of equation. Are they all linear? Occurring over a field? Feb 21, 2019 at 18:32
• I'm talking about linear equations Feb 21, 2019 at 18:33
• The solution can only be unique , if we have at least as many equations than variables. This can be shown by looking at the poosible ranks of the coefficient matrix. Feb 21, 2019 at 18:44