How do you solve the following system?:  -4x + y = 2 , 2x – y = -4

Apr 5, 2018

$y = 6$ and $x = 1$

Explanation:

$- 4 x + y = 2$ ---------(1)
$2 x - y = - 4$ ----------(2)

Multiply equation (1) by $1$ and equation (2) by $2$

$- 4 x + y = 2$ ------------(3)
$4 x - 2 y = - 8$ ------------(4)

Add equation (1) to equation (2)

$0 - y = - 6$

Divide through by $- 1$

$y = 6$ (answer)

Substitute the value of y into equation (1)

$- 4 x + y = 2$

$- 4 x + 6 = 2$

Collect like terms

$- 4 x = 2 - 6$

$- 4 x = - 4$

Divide through by $- 4$

$x = 1$ (answer)