We are given the system of equations and asked to solve it using the substitution method.
[tex]\begin{gathered} \begin{cases}6x+7y=19 \\ 5x+2y=-11\end{cases} \\ 6x+7y=19 \\ 7y=-6x+19 \\ y=-\frac{6}{7}x+\frac{19}{7} \\ 5x+2(-\frac{6}{7}x+\frac{19}{7})=-11 \\ 5x-\frac{12}{7}x+\frac{38}{7}=-11 \\ \frac{23}{7}x+\frac{38}{7}=-11 \\ 23x+38=-77 \\ 23x=-115 \\ x=-5 \\ 5(-5)+2y=-11 \\ -25+2y=-11 \\ 2y=14 \\ y=7 \\ \boxed{(-5,7)} \end{gathered}[/tex]