We are given a system of two linear equations with two variables, $x$ and $y$. We need to find the values of $x$ and $y$ that satisfy both equations. The system of equations is: $4x + 3y = -12$ $-4x + y = 12$

1. Problem Description

We are given a system of two linear equations with two variables, $x$ and $y$. We need to find the values of $x$ and $y$ that satisfy both equations.

The system of equations is:

$4x + 3y = -12$

$-4x + y = 12$

2. Solution Steps

We can solve this system of equations using the method of elimination. We can add the two equations to eliminate the $x$ variable.

Adding the equations:

$(4x + 3y) + (-4x + y) = -12 + 12$

$4x - 4x + 3y + y = 0$

$4y = 0$

Dividing both sides by 4:

$y = \frac{0}{4}$

$y = 0$

Now that we have the value of $y$, we can substitute it back into either of the original equations to solve for $x$. Let's use the first equation:

$4x + 3y = -12$

$4x + 3(0) = -12$

$4x + 0 = -12$

$4x = -12$

Dividing both sides by 4:

$x = \frac{-12}{4}$

$x = -3$

Thus, the solution is $x = -3$ and $y = 0$.

3. Final Answer

$x = -3$

$y = 0$

The solution to the system of equations is $(-3, 0)$.