Answer
$x=2, $ $t=\dfrac{1}{10}$
Work Step by Step
Operating on the corresponding elements, the given matrix equation, $ \begin{bmatrix}
2 & 4
\\
8 & 4.5
\end{bmatrix}
=
\begin{bmatrix}
4x-6 & -10t+5
\\
4x & 15t+1.5x
\end{bmatrix}
,$ implies the following equations:
\begin{align*}
\begin{array}{cc}
2=4x-6 &&4=-10t+5
\end{array}
.\end{align*}
Simplifying the equations above results to
\begin{align*}
\begin{array}{cc}
2+6=4x-6+6 &&4-5=-10t+5-5
\\
8=4x &&-1=-10t
\\
\dfrac{8}{4}=\dfrac{4x}{4} &&\dfrac{-1}{-10}=\dfrac{-10t}{-10}
\\
2=x &&\dfrac{1}{10}=t
\end{array}
.\end{align*}
Hence, $
x=2, $ $t=\dfrac{1}{10}
$.