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**pickslides** $\displaystyle (a + b)x + cy = bc$...(1)

$\displaystyle (b + c)y + ax = -ab$...(2)

Working on (1) to make x the subject

$\displaystyle (a + b)x + cy = bc$

$\displaystyle (a + b)x = bc-cy$

$\displaystyle x = \frac{bc-cy}{a+b}$

Now sub this into (2) for x

$\displaystyle (b + c)y + ax = -ab$

$\displaystyle (b + c)y + a\left(\frac{bc-cy}{a+b}\right) = -ab$

exapnding in the a and separately dividing the denominators

$\displaystyle (b + c)y + \left(\frac{abc}{a+b}\right) - \left(\frac{acy}{a+b}\right)= -ab$

Grouping the y terms together

$\displaystyle (b + c)y - \left(\frac{acy}{a+b}\right)+\left(\frac{abc}{a+b} \right) = -ab$

Taking out y as a common factor

$\displaystyle y\left((b + c) - \left(\frac{ac}{a+b}\right)\right)+\left(\frac{abc }{a+b}\right) = -ab$

$\displaystyle y\left((b + c) - \left(\frac{ac}{a+b}\right)\right) = -ab-\left(\frac{abc}{a+b}\right)$

and finally dividing

$\displaystyle y = \frac{-ab-\left(\frac{abc}{a+b}\right)}{\left((b + c) - \left(\frac{ac}{a+b}\right)\right)}$

You can simplify further and sub back in to find x.