# How do you solve for x in (a+b)x + cy = bc?

Apr 25, 2016

$x = \frac{c \left(b - y\right)}{a + b}$
$\textcolor{w h i t e}{\text{XXXXXXXXX}} \mathmr{if} \left(a + b\right) \ne 0$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} \left(a + b\right) x + c y = b c$

$\Rightarrow$
$\textcolor{w h i t e}{\text{XXX}} \left(a + b\right) x = b c - c y$

$\textcolor{w h i t e}{\text{XXX}} x = \frac{c \left(b - y\right)}{a + b}$ (provided $\left(a + b\right) \ne 0$)