Given the system of equations :
[tex]\begin{gathered} 4x+5y=19\rightarrow(1) \\ 8x-6y=-10\rightarrow(2) \end{gathered}[/tex]Multiply the first equation by -2:
[tex]\begin{gathered} -2\cdot4x+(-2)\cdot5y=-2\cdot19 \\ -8x-10y=-38\rightarrow(3) \end{gathered}[/tex]Add the equations (2) and (3) to eliminate x :
[tex]\begin{gathered} 8x-8x-6y-10y=-10-38 \\ -16y=-48 \\ \\ y=\frac{-48}{-16}=3 \end{gathered}[/tex]Substitute with y in equation (1) to find x :
[tex]\begin{gathered} 4x+5\cdot3=19 \\ 4x+15=19 \\ 4x=19-15 \\ 4x=4 \\ \\ x=\frac{4}{4}=1 \end{gathered}[/tex]So, the solution of the system is :
[tex]\begin{gathered} x=1 \\ y=3 \\ (x,y)=(1,3) \end{gathered}[/tex]