# How do you solve x-2y=4 and -x+6y=12?

Dec 1, 2015

color(green)(x = 12
color(green)(y = 4

#### Explanation:

$x - 2 y = 4$ -----(1)
$- x + 6 y = 12$ ------(2)

The question is asking us the find the values of x and y which satisfy both these equations

To find the value of $x$, we just need to eliminate $y$

We can do that by adding the two equations. We get:

$\left(x - 2 y\right) + \left(- x + 6 y\right) = 4 + 12$

$\to \cancel{x} - 2 y - \cancel{x} + 6 y = 16$

$4 y = 16$

color(green)(y = 4

To get the value of $x$, we can easily substitute this value of $y$ in any of the two equations

Substituting it in the first equation, we get

$x - 2 \left(4\right) = 4$

$\to x - 8 = 4$

Transposing $8$ to the other side, we get

$\to x = 4 + 8$

color(green)(x = 12