# How do you solve for y in Ax - By = C?

$y = \frac{- C + A x}{B}$
We begin with $A x - B y = C$. Our goal is to isolate $y$, and the step I would do is to subtract $A x$ on both sides. If we do that, we have $- B y = C - A x$. From here we need to undo the $- B \cdot y$, so we should divide by $- B$. Now, I like to break this up into two steps just so I don't make any silly mistakes. So first I divide by $- 1$ on both sides, which gives us $B y = \frac{C - A x}{-} 1$ or $B x = - C + A x$. Now I just divide by $B$ on both sides, which leaves us with $y = \frac{- C + A x}{B}$.