# How do you solve the following system: -6x-2y=-14, 4x-5y= -1 ?

Sep 29, 2017

$x = \left(\frac{34}{19}\right)$ & $y = \left(\frac{31}{19}\right)$

#### Explanation:

$6 x + 2 y = 14$
$3 x + y = 7$ (Equation 1)
$4 x - 5 y = - 1$ (Equation 2)
Multiply Equation 1 by 5
$15 x + 5 y = 35$ (Equation 3)
Add Equation 2. & Equation 3
$19 x = 35 - 1 = 34$
$x = \left(\frac{34}{19}\right)$
Substituting value of x in Equation 1,
$3. \left(\frac{34}{19}\right) + y = 7$
$y = 7 - 3 \left(\frac{34}{19}\right)$
$y = \left(133 - 102\right) 19 = \frac{31}{19}$