Answer
$x=-7
\text{ and }
y=3
$
Work Step by Step
Equating the real parts and equating the imaginary parts, the given equation, $
2x+3yi=-14+9i
,$ implies
\begin{align*}
2x&=-14
\\\\&\text{ and }\\\\
3y&=9
.\end{align*}
Solving each equation results to
\begin{align*}
2x&=-14
\\
\dfrac{2x}{2}&=-\dfrac{14}{2}
\\
x&=-7
\\\\&\text{ and }\\\\
3y&=9
\\
\dfrac{3y}{3}&=\dfrac{9}{3}
\\
y&=3
.\end{align*}
Hence, $
x=-7
\text{ and }
y=3
$.
