How do you solve for $y$ : $4 x - 3 y = 12$ ?

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Solution

Determine the value of $y$ :
$4 x - 3 y = 12$
Subtract $4 x$ from both the sides:
$\Rightarrow 4 x - 3 y - 4 x = 12 - 4 x \Rightarrow - 3 y = 12 - 4 x$
Divide by $- 3$ on both sides:
$\begin{array}{rcl} \frac{- 3 y}{- 3} & = & \frac{12 - 4 x}{- 3} \\ \Rightarrow & y = \frac{12}{- 3} - \frac{4 x}{- 3} \\ \Rightarrow & y = - 4 + \frac{4 x}{3} \\ \Rightarrow & y = \frac{4}{3} x - 4 \end{array}$
Hence, the value of $y$ is $\frac{4}{3} x - 4$ .

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