Two positive numbers differ by 11. when the larger number is divided by the smaller, the quotient is 2 and the remainder is 4. what are the numbers

X = larger number 
y = smaller number 

Equations: 

x - y = 11 
x/y = 2 + 4/y 

Get rid of fractions in second equation by multiplying by y. 

y(x/y = 2 + 4/y) 
x = 2y + 4 > plug this into the first equation. 

Solve for y and then x.