How do solve the following linear system?:  -9x + 6y = -2 , 11x + 3y + 7 = 0 ?

Jan 26, 2016

1) multiply the second equation by 2
$22 x + 6 y + 14 = 0$

2) set the first equation equal to $0$ then make both equations equal to each other
$22 x + 6 y + 14 = - 9 x + 6 y + 2$

3) move everything to one side and sum it up
$31 x + 12 = 0$
$31 x = - 12$
$x = - \frac{12}{31}$

4) insert $x$ into the first equation and you get
$\frac{- 9 \cdot \left(- 12\right)}{31} + 6 y = - 2$
$6 y = \frac{\left(- 2 \cdot 31\right) - 9 \cdot 12}{31}$
$y = \frac{\left(- 2 \cdot 31\right) - 9 \cdot 12}{6 \cdot 31}$
$y = \frac{- 31 - 54}{93} = - \frac{85}{93}$