How do you solve the following system?: 21x +14y = 3 , -14x - 59y = -12

Jun 15, 2018

$x = - \frac{351}{623}$ and $y = \frac{30}{89}$

Explanation:

$2 \cdot \left(21 x + 14 y\right) + 3 \cdot \left(- 14 x - 59 y\right) = 2 \cdot 3 + 3 \cdot \left(- 12\right)$

$42 x + 28 y - 42 x - 117 y = 6 - 36$

$- 89 y = - 30$, so $y = \frac{- 30}{- 89} = \frac{30}{89}$

Hence,

$- 14 x - 59 \cdot \frac{30}{89} = - 12$

$- 14 x - \frac{1770}{89} = - 12$

$- 1246 x - 1770 = - 1068$

$- 1246 x = 702$

$x = \frac{702}{- 1246} = - \frac{351}{623}$