Answer
$x-9y=-27$
Work Step by Step
In the form $Ax+By=C,$ where $A,$ $B,$ and $C$ are integers, the given equation is equivalent to:
\begin{align*}
3\left( \dfrac{2}{3}x+3\right)&=(6y-15)3
\\\\
2x+9&=18y-45
\\
2x-18y&=-45-9
\\
2x-18y&=-54
\\\\
\dfrac{1}{2}(2x-18y)&=-54\left(\dfrac{1}{2}\right)
\\\\
x-9y&=-27
\end{align*}