[tex]\text{Solve the systems of equations:}\\\\\frac{1}{5}m-\frac{1}{6}n=0 \\5m-4n=2 \\\\5(\frac{1}{5}m)=(\frac{1}{6}n)5\\\\m=\frac{5}{6}n\\\\\text{Plug in into one of the equations}\\\\5(\frac{5}{6}n)-4n=2\\\\\frac{25}{6}n-4n=2\\\\\frac{1}{6}n=2\\\\\text{Multiply both sides by 6}\\\\\boxed{n = 12}\\\\\text{Now plug in 12 to n in any of the equations}\\\\5m-4(12)=2\\\\5m-48=2\\\\5m=50\\\\\text{Divide:}\\\\\boxed{m=10}[/tex]
