# Simultaneous equation ???

Mar 14, 2017

The solution of the system of linear equations:

$\left\{\begin{matrix}\left(\frac{1}{2} x + y\right) = 5 \\ x - 2 y = 6\end{matrix}\right.$

is:

$\left\{\begin{matrix}x = 8 \\ y = 1\end{matrix}\right.$

#### Explanation:

We have a system of linear equations in two unknowns:

$\left\{\begin{matrix}\left(\frac{1}{2} x + y\right) = 5 \\ x - 2 y = 6\end{matrix}\right.$

We can solve it by substitution: from the second equation we have:

$x = 6 + 2 y$

Substituting this expression in the first equation we have:

$\frac{1}{2} \left(6 + 2 y\right) + y = 5$

$3 + y + y = 5$

$2 y = 5 - 3$

$2 y = 2$

$y = 1$

and then:

$x = 6 + 2 = 8$