How do you solve by substitution x - y = 6 and x + y = -2?

Jun 7, 2015

$x - y = 6$
Thus color(blue)(x=6+y ( we add $y$ on both side )

Now that we have $\textcolor{b l u e}{x}$, we can replace it in the second equation :

$\textcolor{b l u e}{x} + y = - 2$
$\textcolor{b l u e}{6 + y} + y = - 2$
$6 + 2 y = - 2$
$2 y = - 2 - 6$ ( we substract $6$ on each side )
$2 y = - 8$
color(red)(y=-4 ( we divide by $2$ on each side )

Now that we have $\textcolor{red}{y}$, we can find $\textcolor{b l u e}{x}$ :

$\textcolor{b l u e}{x} = 6 + \textcolor{red}{y}$
$\textcolor{b l u e}{x} = 6 \textcolor{red}{- 4}$
$\textcolor{b l u e}{x = 2}$