[tex]\bf \begin{cases}
6x+2y=-78\\
7x-4y=-15
\end{cases}\qquad \begin{bmatrix}
6&2\\7&-4
\end{bmatrix}\implies (6\cdot -4)-(7\cdot 2)\implies \stackrel{D}{\boxed{-38}}\\\\
-------------------------------\\\\
x=\cfrac{D_x}{D}\implies \cfrac{
\begin{bmatrix}
-78&2\\-15&-4
\end{bmatrix}}{-38}\implies \cfrac{(-78\cdot -14)-(-15\cdot 2)}{-38}
\\\\\\
\cfrac{312+30}{-38}\implies\cfrac{342}{-38} \implies -9\\\\
-------------------------------[/tex]
[tex]\bf y=\cfrac{D_y}{D}\implies \cfrac{
\begin{bmatrix}
6&-78\\7&-15
\end{bmatrix}}{-38}\implies \cfrac{(6\cdot -15)-(-7\cdot 78)}{-38}
\\\\\\
\cfrac{-80+546}{-38}\implies \cfrac{456}{-38}\implies -12[/tex]
