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

Mar 18, 2017

$\left(- 2 , 5\right)$

#### Explanation:

$3 x + 2 y = 4$
$4 x + 3 y = 7$
Multiply the 1st and 2nd equations by 3 and -2 respectively:
$9 x + 6 y = 12$
$- 8 x - 6 y = - 14$ => add the equations y's cancel, solve for x:
$x = - 2$ => plug in the 1st equation solve for y:
$- 6 + 2 y = 4$
$2 y = 10$
$y = 5$
Hence the solution set is:
$\left(x , y\right) = \left(- 2 , 5\right)$