The given system of equations is
[tex]\begin{gathered} 6x+y=5 \\ -8x-5y=19 \end{gathered}[/tex]To solve the system, first, let's multiply the first equation by 5.
[tex]\begin{gathered} 30x+5y=25 \\ -8x-5y=19 \end{gathered}[/tex]Then, we combine the equations
[tex]\begin{gathered} 30x-8x+5y-5y=25+19 \\ 22x=44 \\ x=\frac{44}{22} \\ x=2 \end{gathered}[/tex]Now, we find y
[tex]\begin{gathered} 6x+y=5 \\ 6\cdot2+y=5 \\ 8+y=5 \\ y=5-8 \\ y=-3 \end{gathered}[/tex]