# How do you solve the following system?:  1/2x=y-1 , -x+3y=-7

Apr 24, 2018

$x = - 20$

$y = - 9$

#### Explanation:

The given equations are

$\frac{1}{2} x = y - 1$
$- x + 3 y = - 7$

From $\frac{1}{2} x = y - 1$

$x = 2 \left(y - 1\right)$

Substituting this $x$ value in equation $- x + 3 y = - 7$

=> - (2(y-1) + 3y = -7

$\implies - 2 y + 2 + 3 y = - 7$

$\implies y + 2 = - 7$

$\implies y = - 7 - 2$

$\implies y = - 9$

Substitute this $y$ value in any of the given equations to obtain the $x$ value

$- x + 3 y = - 7$

$\implies - x + 3 \left(- 9\right) = - 7$

$\implies - x - 27 = - 7$

$\implies x = - 20$