I find it easier to start from scratch and write out the equations, then compare them with the given equations.
Let m and j represent the ages of the two boys. Then m-5=(2/3)(j-5) Also, in ten years: m+10 = (5/6)j.
Let's solve this system: Mult the first eqn by 3 to remove the fraction: 3(m-5) = 2(j-5), or 3m - 15 = 2j -10. Next, mult. the 2nd eqn by 6 to remove the fraction: 6m+60 = 5j.
Our two equations are (at this point) 3 m - 15 = 2j - 10 and 6m +60 = 5j
Let's mult. the first equation by -2, so as to obtain the coefficient -6 for m: