# How do you solve by substitution x-y=-4 and x+3y=4?

Jun 11, 2015

The solution for the system of equations is
 color(red)(x = -2 , y=2

#### Explanation:

$x - y = - 4$
 x =color(red)( -4+y  .....equation $\left(1\right)$
$x + 3 y = 4$........equation $\left(2\right)$

Substituting equation $1$ in $2$ to find $x$
$x + 3 y = 4$
$\textcolor{red}{- 4 + y} + 3 y = 4$
$- 4 + 4 y = 4$
$4 y = 8$
 color(red)(y=2

Substituting $y$ in equation $1$ to obtain $x$:
$x = - 4 + y$
$x = - 4 + 2$
color(red)( x=-2

Jun 11, 2015

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

#### Explanation:

Given:
[1]$\textcolor{w h i t e}{\text{XXXX}}$$x - y = - 4$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$x + 3 y = 4$

We can rewrite [1] as
[3]$\textcolor{w h i t e}{\text{XXXX}}$$x = y - 4$
then substituting the expression $y - 4$ from [3] in place of $x$ in [2]
[4]$\textcolor{w h i t e}{\text{XXXX}}$$\left(y - 4\right) + 3 y = 4$
which simplifies as
[5]$\textcolor{w h i t e}{\text{XXXX}}$$4 y = 8$
or
[6]$\textcolor{w h i t e}{\text{XXXX}}$$y = 2$
substituting $2$ for $y$ in [1], we get
[7]$\textcolor{w h i t e}{\text{XXXX}}$$x - 2 = - 4$
[8]$\textcolor{w h i t e}{\text{XXXX}}$$x = - 2$