# How do you solve the following system?: 3x -9y =-13 , -2x +17y = 8

Apr 29, 2016

$x = - \frac{139}{69}$
$y = \frac{50}{69}$

#### Explanation:

$3 x - 9 y = - 13$ and
$- 2 x + 17 y = 8$

multiply first statement by "2" and the second statement by "3" to get to a common coefficient of 'x'
$2 \left(3 x - 9 y\right) = 2 \left(- 13\right)$
$3 \left(2 x + 17 y\right) = 3 \left(8\right)$

$6 x - 18 y = - 26$
$6 x + 51 y = 24$

then, subtract second statement from first statement
$- 69 y = - 50$

now that y is isolated, we know that
$y = \frac{50}{69}$

to solve for x, substitute the value for 'y' into one of the statements

$3 x - 9 \left(\frac{50}{69}\right) = - 13$

divide the statement by 3
$x - 3 \left(\frac{50}{69}\right) = - \frac{13}{3}$
$x - \left(\frac{50}{23}\right) = - \frac{13}{3}$
$x = - \frac{13}{3} + \frac{50}{23}$

lastly, solve for lowest common denominator
$x = \frac{- 299 + 150}{69} = - \frac{139}{69}$