# How do solve the following linear system?:  x + y = 2, 3x + 2y = 12?

Feb 3, 2017

Elimination is my favorite

#### Explanation:

( $x + y = 2$ ) $\cdot 2$ (Times the equation by two)

$2 x + 2 y = 4$

Now subtract the equalities:
$\textcolor{b l u e}{3 x} + \textcolor{red}{\cancel{2 y}} = \textcolor{g r e e n}{12}$
$\textcolor{b l u e}{2 x} + \textcolor{red}{\cancel{2 y}} = \textcolor{g r e e n}{4}$
$\textcolor{b l u e}{x} + \textcolor{red}{0 y} = \textcolor{g r e e n}{8}$

so $x = 8$

Thus, $y = - 6$ (by plugging $x = 8$ into an original equation)