Answer
$\left\{\begin{matrix}
2x& -3y &=&8 \\
5x& +6y &=&11
\end{matrix}\right.$
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.
$\Rightarrow D=\begin{vmatrix}
2 &-3 \\
5&6
\end{vmatrix}=\begin{vmatrix}
a_1 &b_1 \\
a_2&b_2
\end{vmatrix}$
Here we have $a_1=2,b_1=-3,a_2=5$ and $b_2=6$.
and
$\Rightarrow D_x=\begin{vmatrix}
8 &-3 \\
11&6
\end{vmatrix}=\begin{vmatrix}
c_1 &b_1 \\
c_2&b_2
\end{vmatrix}$
Here we have $c_1=8,b_1=-3,c_2=11$ and $b_2=6$.
Plug all values into the system of equations.
$\Rightarrow \left\{\begin{matrix}
2x& -3y &=&8 \\
5x& +6y &=&11
\end{matrix}\right.$
