Like you said, we will use substitution to solve the system to get rid of y.
[tex]y = -6x - 19\\6x - 5y = -13\\\\6x - 5(-6x - 19) = -13\\\\6x + 30x + 95 = -13\\\\36x + 95 = -13\\\\36x = -108\\\\x = -3[/tex]
Next, we will use what we found for x and plug it into one of the original equations to solve for y. I will use the first equation.
[tex]y = -6(-3) - 19\\\\y = 18 - 19\\\\y = -1[/tex]
Finally, we can now create the solution for this system.
[tex](-3, -1)[/tex]
