Answer
$ \left\{\begin{matrix}
2x& -4y &=&8 \\
3x& +5y &=&-10
\end{matrix}\right.$
Work Step by Step
Let the system of equations be
$\Rightarrow \left\{\begin{matrix}
a_1x& +b_1y &=&c_1 \\
a_2x& +b_2y &=&c_2
\end{matrix}\right.$
The given determinants are.
$\Rightarrow D=\begin{vmatrix}
2 &-4 \\
3&5
\end{vmatrix}=\begin{vmatrix}
a_1 &b_1 \\
a_2&b_2
\end{vmatrix}$
Here we have $a_1=2,b_1=-4,a_2=3$ and $b_2=5$.
and
$\Rightarrow D_x=\begin{vmatrix}
8 &-4 \\
-10&5
\end{vmatrix}=\begin{vmatrix}
c_1 &b_1 \\
c_2&b_2
\end{vmatrix}$
Here we have $c_1=8,b_1=-4,c_2=-10$ and $b_2=5$.
Plug all values into the system of equations.
$\Rightarrow \left\{\begin{matrix}
2x& -4y &=&8 \\
3x& +5y &=&-10
\end{matrix}\right.$
