# How do you solve the system 4x - y = 5 and x + y = 10?

Jun 8, 2015

$x + y = 10$
Thus : color(blue)(x=10-y ( we substract $\textcolor{red}{y}$ on each side )

We can now replace it in the first equation :

$4 \textcolor{b l u e}{x} - y = 5$
$4 \cdot \textcolor{b l u e}{\left(10 - y\right)} - y = 5$
$40 - 4 y - y = 5$
$40 - 5 y = 5$
$40 = 5 + 5 y$ ( we add $5 y$ on each side )
$40 - 5 = 5 y$ ( we substract $5$ on each side )
$35 = 5 y$
color(red)(y=7 ( we divide by $5$ on each side )

We can now calculate $\textcolor{b l u e}{x}$ with $\textcolor{red}{y}$ :

$\textcolor{b l u e}{x} = 10 - \textcolor{red}{y}$
$\textcolor{b l u e}{x} = 10 - \textcolor{red}{7}$
$\textcolor{b l u e}{x = 3}$