Question

The difference of two numbers is 2. Their sum is 18. Find the numbers.

Answer 1

$x + y = 18 \\ x - y = 2 \\ on \: adding \: both \: the \: equations \: we \: get \\ (x + y) + (x - y) = 18 + 2 \\ = x + y + x -y = 20\\ = x + x = 20 \\ = 2x = 20 \\ = x = \frac{20}{2} \\ = x = 10 \\ put \: x = 10 \: in \: any \: equation \\ x + y = 18 \\ 10 + y = 18 \\ y = 18 - 10 \\ y = 8 \\ hence \: x = 10 \: and \: y = 8$

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