Answer
$x=\dfrac{16}{3}
\text{ and }
y=-\dfrac{19}{8}
$
Work Step by Step
Equating the real parts and equating the imaginary parts, the given equation, $
3x+19i=16-8yi
,$ implies
\begin{align*}
3x&=16
\\\\&\text{ and }\\\\
19&=-8y
.\end{align*}
Solving each equation results to
\begin{align*}
3x&=16
\\
\dfrac{3x}{3}&=\dfrac{16}{3}
\\
x&=\dfrac{16}{3}
\\\\&\text{ and }\\\\
19&=-8y
\\
\dfrac{19}{-8}&=\dfrac{-8y}{-8}
\\
-\dfrac{19}{8}&=y
.\end{align*}
Hence, $
x=\dfrac{16}{3}
\text{ and }
y=-\dfrac{19}{8}
$.
