# How do solve the following linear system?:  x+2y=1 , x+y=6 ?

Nov 28, 2015

$\left(11 , - 5\right)$

#### Explanation:

Equation 1: $x + 2 y = 1$
Equation 2 : $x + y = 6$

To solve by substitution method, take equation 1, solve for $x$
$x + 2 y = 1$ $\Leftrightarrow \textcolor{red}{x = 1 - 2 y}$

Then substitute $\textcolor{red}{x = 1 - 2 y}$ into equation 2

$\implies \textcolor{red}{\left(1 - 2 y\right)} + y = 6$

$\implies 1 - y = 6$
$\implies - y = 5$ $\implies \textcolor{b l u e}{y = - 5}$

Substitute the solution for $y$ into either equation 1 equation 2

$\implies x + 2 \textcolor{b l u e}{\cdot} \left(\left(- 5\right)\right) = 1$
$\implies x - 10 = 1$ $\implies \textcolor{b l u e}{x = 11}$

We can verify the solution by substitute the solution into the original equations

Eq 1: $\left(11\right) + 2 \left(- 5\right) = 1$
$\implies 1 = 1$

Eq 2: $11 + \left(- 5\right) = 6$
$\implies 6 = 6$