Solving by substitution method.
We have 2 equations:
[tex]y=-2x-9[/tex]and
[tex]6x-5y=-19[/tex]If we substitute the first equation into the second one, we get
[tex]6x-5(-2x-9)=-19[/tex]which gives
[tex]\begin{gathered} 6x-5(-2x)-5(-9)=-19 \\ 6x+10x+45=-19 \\ 6x+45=-19 \\ 6x=-19-45 \\ 6x=-64 \\ x=-\frac{64}{6} \\ x=-10.666 \end{gathered}[/tex]Now, we can substitute this result into the first equation, then we get
[tex]y=-2(-10.66)-9[/tex]then, we have
[tex]\begin{gathered} y=21.33-9 \\ y=12.33 \end{gathered}[/tex]Therefore, the solution of the system is
[tex]\begin{gathered} x=-10.66 \\ \text{and} \\ y=12.33 \end{gathered}[/tex]