# How do you solve the system 3x - 4y = -1 and 9x + 12y = 15?

May 23, 2015

Isolate one variable in one equation and then substitute it in the other equation.

Let's, for example, isolate $y$ in the second equation:

$y = \frac{15}{12} - \frac{9 x}{12} = \frac{5}{4} - \frac{3 x}{4} = \frac{5 - 3 x}{4}$

Substituting it in the other equation (that is, the first one):

$3 x - \cancel{4} \frac{5 - 3 x}{\cancel{4}} = - 1$
$3 x - 5 + 3 x = - 1$
$6 x = 4$
$x = \frac{2}{3}$

If $x = \frac{2}{3}$ and $y = \frac{5 - 3 x}{4}$, then,

$y = \frac{5 - \cancel{3} \left(\frac{2}{\cancel{3}}\right)}{4} = \frac{5 - 2}{4} = \frac{3}{4}$