Question

Find two numbers with a sum of 20 and a difference of 14.

Answer 1

Let these two numbers be $x$ and $y$. Clearly, $x\neq y$, because $|x-y|=0\neq14$. Let's assume $x<y$. Then

$\begin{cases}x+y=20\\y-x=14\end{cases}$


From the second equation, we can obtain $y=x+14$, so substituting for $y$ in the first equation gives


$x+(x+14)=2x+14=20\implies 2x=6\implies x=3$

which means $y=3+14=17$.