# How do you solve the system 4x - 3y = 34, 3x + 9y = -42?

Feb 22, 2016

Using Gaussian elimination, add three times the first equation to the second equation to leave an expression just in $x$. substitute this back into one of the equations to find $y$.

#### Explanation:

$4 x - 3 y = 34$
$3 x + 9 y = - 42$

Equation $1$ times $3$ gives
$12 x - 9 y = 102$

Adding this to equation $2$ gives
$15 x = 60$

$\therefore x = 4$

$4 \cdot 4 - 3 y = 34$
3y = 16 - 34 = - 18#

$\therefore y = - 6$