# How do you solve the system 3x+2y=4 and 4x+3y=7?

Mar 25, 2018

$x = - 2$ and $y = 5$

#### Explanation:

You can begin by subtracting the first equation from the second, which simplifies your operations. Doing so leaves you with $x + y = 3$.

You can write $x$ as $x = 3 - y$ and substitute in whichever equation you prefer:
$4 \left(3 - y\right) + 3 y = 7$
$12 - 4 y + 3 y = 7$
$12 - y = 7$
$- y = 7 - 12 = - 5$
$y = 5$

After finding $y$ you can return to $x = 3 - y$ and substitute $y$.

$x = 3 - 5$
$x = - 2$

So your solution is $S = \left\{\left(- 2 , 5\right)\right\}$