Paco had 41 cookies. He gave 9 cookies to his friend and ate 18 cookies. How many more cookies did he eat than those he gave to his friend?
There are two people in the problem, so we will introduce two variables: $x$ will denote the number of cookies that the first person ate, and $y$ will denote the number of cookies that the second person ate. 

We are told that the first person ate $5$ more cookies than the second person. In symbols:

$$x = y + 5$$

We are also told that the first person gave away $4$ cookies to the second person. In symbols:

$$x - 4 = y$$

We can solve this system for $x$ and $y$. We will use substitution:

$$\begin{align*}
x &= y + 5\\
x - 4 &= y\\
\end{align*}$$

Subtracting the second equation from the first equation, we get:

$$x - (x - 4) = y + 5 - y$$

Cancelling out like terms, we get:

$$4 = 5$$

This is not true, so there is no solution to the system.