If 12x + 13y = 29 and 13x + 12y = 21, find x + y.

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Solution

We have:
12x + 13y = 29 ...(1)
and
13x + 12y = 21 ...(2)
Adding both equations, we get:
12x + 13y = 29
13x + 12y = 21
------------------------
25x + 25y = 50
⇒ 25( x + y) = 50
$\Rightarrow x + y = \frac{50}{25} ∴ x + y = 2$

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