Example3.3.7

Solve for \(y\) in \(2x+5y=10\text{.}\) (This is a linear equation in standard form.)

To solve for \(y\) in the equation \(2x+5y=10\text{,}\) we will first have to solve for \(5y\text{.}\) We'll do so by subtracting \(2x\) from each side of the equation. After that, we'll be able to divide each side by \(5\) to finish solving for \(y\text{:}\)

\begin{align*} 2x+5\attention{y}\amp=10\\ 2x+5\attention{y}\subtractright{2x}\amp=10\subtractright{2x}\\ 5\attention{y}\amp=10-2x\\ \divideunder{5\attention{y}}{5}\amp=\divideunder{10-2x}{5}\\ y\amp=\frac{10-2x}{5} \end{align*}
in-context