# How do you solve the system 3x + y = 5 and -2x + 3y =4?

Jun 6, 2017

$x = 1$
$y = 2$

#### Explanation:

First you would multiply each equation by the coefficient of x

$- 2 \left(3 x + y = 5\right)$
$3 \left(- 2 x + 3 y = 4\right)$

Which is simplified to

$- 6 x - 2 y = - 10$
$- 6 x + 9 y = 12$

Then you would minus both equations together cancelling $x$ to get the value of $y$

$- 11 y = - 22$

$y = \frac{22}{11}$

$y = 2$

Put 2 in replace of $y$ into one of the original equation to find x

$3 x + 2 = 5$

$3 x = 5 - 2$

$x = \frac{5 - 2}{3}$

$x = 1$