Question

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

Answer 1

Hint: Here, we need to make y as a subject in simple words. We begin with $Ax - By = C$ . Our goal is to isolate y, and the step one would do is to subtract $Ax$ on both sides. If we do that, we have $ - By = C - Ax$. From here we need to undo the $ - B \times y$. So we should divide by $ - B$. So first we divide by $ - 1$ on both sides, which gives us $By = \dfrac{{C - Ax}}{{ - 1}}$ or $By = - C + A$. Now we just divide by B into both sides, which leaves us with
$y = \dfrac{{ - C + Ax}}{B}$.

Complete step by step answer:
The aim in solving for y is to get y on one side by itself :
$Ax - By = C$
$\Rightarrow$ $Ax - C = By$
$\Rightarrow$ $\dfrac{{Ax - C}}{B} = y$

$\therefore y = \dfrac{{Ax - C}}{B}$.

Note: The coefficient of the x-term should be a positive integer value, so we multiply the entire equation by an integer value that will make the coefficient positive, as well as, all of the coefficients integers. This gives us the standard form. To find the x-intercept of a given linear equation, simply remove the 'y' and solve for 'x'. To find the y-intercept, remove the 'x' and solve for 'y'.
A slope-intercept form equation is when it is set up $y = mx + b$. In order to go from one form to another, all we have to do is change the order of the given numbers. First, we want to move the $Ax$ to the opposite side of the equation, by either adding or subtracting it.