Help me Please

$\frac{12}{x}+\frac5y=8\\ \frac8x-\frac3y=-1$

                                           This is the same as....

$12(\frac1x)+5(\frac1y)=8 \\ 8(\frac1x)-3(\frac1y)=-1$

                                           Multiply the top equation through by  2 , and

                                           multiply the bottom equation through by  -3 .

$24(\frac1x)+10(\frac1y)=16 \\ -24(\frac1x)+9(\frac1y)=3$

                                           Add the two equations together and solve for  y .

$19(\frac1y)=19 \\ 19=19y\\ \color{Emerald}1=y$

                            Plug in  1  for  y  in one of the original equations to find  x .

$\frac{12}{x}+\frac51=8 \\ \frac{12}x=3 \\ 12=3x\\ \color{Emerald}4=x$