Question

Solve the system:
1 5 m− 1 6 n=0
5m−4n=2

Answer 1

`\text{Solve the systems of equations:}\\\\(1)/(5)m-(1)/(6)n=0 \\5m-4n=2 \\\\5((1)/(5)m)=((1)/(6)n)5\\\\m=(5)/(6)n\\\\\text{Plug in into one of the equations}\\\\5((5)/(6)n)-4n=2\\\\(25)/(6)n-4n=2\\\\(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}`