# What are x and y if 4x-4y=-16 and x-2y=-12?

Nov 10, 2015

$x = 4$, $y = 8$

#### Explanation:

There are many ways to solve a system of linear equations.
One of those goes like this:

Take the equation that looks easier to you and solve it for $x$ or $y$, whichever is easier.
In this case, if I were you, I would definitely take $x - 2 y = - 12$ and solve it for $x$:

$x - 2 y = - 12$
$\iff x = 2 y - 12$

Now, plug $2 y - 12$ for $x$ in the other equation:

$4 \cdot \left(2 y - 12\right) - 4 y = - 16$

...simplify the left side:
$\iff 8 y - 48 - 4 y = - 16$
$\iff 4 y - 48 = - 16$

... add $48$ on both sides:
$\iff 4 y = 48 - 16$
$\iff 4 y = 32$

... divide by 4 on both sides:
$\iff y = 8$

Now that you have the solution for $y$, you just need to plug this value into one of the two equations (again, whichever is easier) and compute $x$:

$x - 2 \cdot 8 = - 12$
$\iff x = 16 - 12$
$\iff x = 4$