# How do you solve the following system: 3x - 2y = 9, 6x + y = 2?

Apr 8, 2016

The solution for the system of equations is:
color(green)(x = 13/15

color(green)(y = (-16)/ 5

#### Explanation:

$3 x - 2 y = 9$, multiplying by $2$
$\textcolor{g r e e n}{6 x} - 4 y = 18$.............equation $\left(1\right)$

$\textcolor{g r e e n}{6 x} + y = 2$.................equation $\left(2\right)$

Solving by elimination.

Subtracting equation $2$ from $1$:

$\cancel{\textcolor{g r e e n}{6 x}} - 4 y = 18$
$- \cancel{\textcolor{g r e e n}{6 x}} - y = - 2$

$- 5 y = 16$

color(green)(y = (-16)/ 5

Finding $x$ from equation $1$

$3 x - 2 y = 9$

$3 x = 9 + 2 y$

$3 x = 9 + 2 \cdot \left(- \frac{16}{5}\right)$

$3 x = 9 - \frac{32}{5}$

$3 x = \frac{45}{5} - \frac{32}{5}$

$3 x = \frac{13}{5}$

$x = \frac{13}{5 \cdot 3}$

color(green)(x = 13/15