# How do you solve the following linear system:  2x + 3y = 2, x + 3y = 9, ?

Apr 3, 2018

$x = - 7 , y = \frac{16}{3}$

#### Explanation:

You may solve the system via substitution:

$2 x + 3 y = 2$
$x + 3 y = 9$

From the second equation you can exctract $x = 9 - 3 y$

Substituting back in the first equation, you have

$2 x + 3 y = 2$
$\setminus \iff$
$2 \left(9 - 3 y\right) + 3 y = 2$
$\setminus \iff$
$18 - 6 y + 3 y = 2$
$\setminus \iff$
$18 - 3 y = 2$
$\setminus \iff$
$16 = 3 y$

And thus $y = \frac{16}{3}$

Once $y$ is known, we can substitute it again into

$x = 9 - 3 y = 9 - 3 \cdot \frac{16}{3} = 9 - 16 = - 7$