# How do solve the following linear system?:  4x-3y=1 , 3x + y = -20 ?

Jan 27, 2016

$x = - \frac{59}{13}$
$y = - \frac{83}{13}$

#### Explanation:

Given -

$4 x - 3 y = 1$ -----------------------------(1)
$3 x + y = - 20$ ---------------------------(2)

Solve the 2nd equation for $y$

$y = - 20 - 3 x$

Substitute $y = - 20 - 3 x$ in equation (1)

$4 x - 3 \left(- 20 - 3 x\right) = 1$
$4 x + 60 + 9 x = 1$
$13 x = 1 - 60$
$x = - \frac{59}{13}$

Substitute $x = - \frac{59}{13}$ in equation (2)

$3 \left(- \frac{59}{13}\right) + y = - 20$
$- \frac{177}{13} + y = - 20$
$y = - 20 + \frac{177}{13} = \frac{- 260 + 177}{13} = - \frac{83}{13}$

$y = - \frac{83}{13}$