# What is the solution for the system of equations 3y + 2x = 4  and 2y-6x=-12 ?

Apr 19, 2018

Multiplying the first by 3 yields $9 y + 6 x = 12$, adding to the second $11 y = 0$ so $y = 0$ and $x = 2$.

Apr 19, 2018

$x = 2$
$y = 0$

#### Explanation:

1. $3 y + 2 x = 4$
2. $2 y - 6 x = - 12$

Multiply the first equation by 3:
$9 y + 6 x = 12$
Sum equation (1.)+(2.):
$9 y + 6 x = 12$ |+
$2 y - 6 x = - 12$
$9 y + 2 y + 6 x - 6 x = 12 - 12$
$11 y + 0 = 0$ $\implies$ $y = 0$

Put $y = 0$ in one equation for example the first:
$3 \cdot 0 + 2 x = 4$
$x = \frac{4}{2} = 2$