Question

if the difference in the side lengths of two squares is 10, and the sum of the side length is 18, what are the side lengths?

Answer 1

Set up the system of equations described in the question, and add the equations:

$x-y=10$ 
$+(x+y=18)$
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$\hspace*{1em} 2x \enspace \enspace \enspace =28 \newline \hspace*{1em} \enspace x \enspace \enspace \enspace =14$

Now that we have x=14, the other side length can be solved by substituting 14 into either equation to get y=4.

The side length of one square is 14. The side length of the other is 4.