# How do you solve the following linear system:  y = - 3x + 8, 2x+3y=5 ?

Nov 12, 2015

$x = \frac{19}{7}$
$y = \frac{- 1}{7}$

#### Explanation:

$y = - 3 x + 8$ -----------------------(1)
$2 x + 3 y = 5$---------------------(2)

Plug in the value of $y = - 3 x + 8$ in equation (2)

$2 x + 3 \left(- 3 x + 8\right) = 5$

$2 x - 9 x + 24 = 5$

$- 7 x = 5 - 24 = - 19$

$x = \frac{- 19}{- 7} = \frac{19}{7}$

$x = \frac{19}{7}$

Substitute $x = \frac{19}{7}$ in equation (1)

$y = - 3 \left(\frac{19}{7}\right) + 8 = \frac{- 57 + 56}{7} = \frac{- 1}{7}$

$y = \frac{- 1}{7}$