Solve Ax + By = −C for x.

Question

Do I make the By negative or do I keep it as it is, add or subtract By and -C, and then divide?

Answer 1

Subtract By from both sides first:

Ax + By - By = -C - By

Ax = -C - By

Then divide both sides by A:

Ax/A = (-C - By) / A

x = (-C - By)/A = -C/A - By/A

Answer 2

Ax + By = -C

So you're looking to isolate x. The first step would be to subtract By from both sides:

Ax + By - By = -C - By

Ax = -By - C (the reorder is because we place the variables before the constants in algebra)

The next step is to divide by A:

Ax / A = (-By - C) / A

x = ^{-By - C}/_A

I suggest you get used to this formula of action as you'll be finding yourself isolating x (and particularly y for linear graphing purposes) a lot.

As an option for the final answer, since we have a negative By and a negative C, we can factor out the negatives:

x = ^{-(By + C)}/_A

x = - ^{By + C}/_A