Question

$99x + 12y = 105$
$12x + 99y = - 6$

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Answer 1

$99x + 12y = 105$

$12x + 99y = - 6$

adding both

$111x + 111y = 99 \\ x + y = \frac{99}{111}$

subtracting 2nd from 1st

$87x - 87y = 111 \\ x - y = \frac{111}{87}$

adding both

$2x = \frac{99}{111} + \frac{111}{87} \\ x = \frac{99}{222} + \frac{111}{174}$

using subtraction

$2y = \frac{99}{111} - \frac{111}{87} \\ y = \frac{99}{222} - \frac{111}{174}$