# How do you solve the system  y=6x - 11 and -2 - 3y = -7 by substitution?

May 25, 2015

Given
$\text{[1] } y = 6 x - 11$
$\text{[2] } - 2 - 3 y = - 7$

from $\text{[1]}$ we can substitute $6 x - 11$ for $y$ in $\text{[2]}$
$\text{[3] } - 2 - 3 \left(6 x - 11\right) = - 7$

$\text{[4] } - 3 \left(6 x - 11\right) = - 5$

$\text{[5] } 6 x - 11 = \frac{5}{3}$

$\text{[6] } 6 x = \frac{38}{3}$

$\text{[7] } x = \frac{19}{9}$

Note that $\text{[2]}$ can be solved directly for $y$
$\text{[8] } - 3 y = - 5$

$\text{[9] } y = \frac{5}{3}$

Query: Was the second equation intended to be
$- 2 x - 3 y = - 7$?