# How do you solve the following system: x-2y=3, 6y + 4x = 12 ?

May 20, 2016

The solution for the system of equations is:
color(green)(x = 3

color(green)(y=0

#### Explanation:

$x - 2 y = 3$, multiplying the equation by $4$

$\textcolor{b l u e}{4 x} - 8 y = 12$...........equation $\left(1\right)$

$\textcolor{b l u e}{4 x} + 6 y = 12$............equation $\left(2\right)$

Solving by elimination:

Subtracting equation $2$ from equation $1$:

$\cancel{\textcolor{b l u e}{4 x}} - 8 y = \cancel{12}$
$- \cancel{\textcolor{b l u e}{4 x}} - 6 y = \cancel{- 12}$

$- 14 y = 0$

$y = \frac{0}{- 14}$

color(green)(y=0

Finding $x$ from equation $1 :$

$x - 2 y = 3$

$x = 3 + 2 y$

$x = 3 + 2 \times 0$

$x = 3 + 0$

color(green)(x = 3