By the way the solution you posted cannot be correct since 11 + 20 = 31 not 36.

Here is how to solve the problem.

\(\displaystyle x + y = 36\)

Let's assume \(\displaystyle x\ge y\) then

\(\displaystyle x = 2y + 3\)

Which come from

If the larger number is divided by the smaller number, the

qoutient is 2 and the remainder is 3.

Now, we can substitute \(\displaystyle 2y + 3\) in for \(\displaystyle x\) which give

\(\displaystyle 2y + 3 + y = 36 \Rightarrow 3y = 33 \Rightarrow y = 11\)

Finally, substitute this back in

\(\displaystyle x = 2\cdot 11 + 3 = 25\)

Answer: 25 and 11