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We can use difference of squares for the first equation to get:

$(a+b)(a-b) = 10$

Then we can substitute our second equation in to get:

$(a+b)(2)=10$

Dividing both sides by 2, we get:

$a+b = 5$

 remember that $a^2 - b^2$ can be factorized into $(a+b)(a-b)$