# How do you solve the following system?: 12x +7y = 3 , 4x + 3y = -2

Nov 13, 2015

$x = 2.875$
$y = - 4.5$

#### Explanation:

$12 x + 7 y = 3$,
$4 x + 3 y = - 2$.

There are (as far as I know) three methods of solving simultaneous equations. I'll choose substitution. Therefore we must leave either $x$ or $y$ alone. I'll choose $x$ in the second equation (you can choose any of the 2 variables in any of the 2 equations):
$4 x + 3 y = - 2$,
$4 x = - 3 y - 2$,
$x = \frac{- 3 y - 2}{4}$.

We now substitute $x$ in the other equation such that:
$12 x + 7 y = 3$,
$12 \left(\frac{- 3 y - 2}{4}\right) + 7 y = 3$, 12 and 4 cancel out,
$3 \left(- 3 y - 2\right) + 7 y = 3$,
$- 9 y - 6 + 7 y = 3$, we now add $y$s and pass the $6$ to the other side,
$- 2 y = 9$,
$2 y = - 9$,
$y = - 4.5$.

We now substitute $y$ by this value in any of the 2 equations. I'll choose the second one:
$4 x + 3 \left(- 4.5\right) = - 2$,
$4 x - 13.5 = - 2$, we now pass $- 13.5$ to the other side,
$4 x = 11.5$,
$x = 2.875$.

Hope it Helps! :D .