# How do solve the following linear system?:  9 x-6y =3 , x + y= 12 ?

Jan 17, 2017

$x = 5$ and $y = 7$

#### Explanation:

$9 x - 6 y = 3$
$x + y = 12$

Using the second equation, determine a value for $y$.

$x + y = 12$

Subtract $x$ from both sides.

$y = 12 - x$

Reduce the first equation by dividing all terms by $3$.

$9 x - 6 y = 3$

$3 x - 2 y = 1$

Substitute $y$ with $\textcolor{red}{\left(12 - x\right)}$.

$3 x - 2 \textcolor{red}{\left(12 - x\right)} = 1$

Open the brackets and simplify. The product of two negatives is a positive.

$3 x - 24 + 2 x = 1$

$5 x - 24 = 1$

Add $24$ to both sides.

$5 x = 25$

Divide both sides by $5$.

$x = 5$

In the second equation, substitute $x$ with $\textcolor{b l u e}{5}$.

$x + y = 12$

$\textcolor{b l u e}{5} + y = 12$

Subtract $5$ from each side.

$y = 7$