We need to solve the following system of linear equations: $x - 3y = -9$ $4x - 2y = -6$

1. Problem Description

We need to solve the following system of linear equations:

$x - 3y = -9$

$4x - 2y = -6$

2. Solution Steps

We can solve this system of equations using substitution or elimination. Let's use elimination.

First, multiply the first equation by -4:

$-4(x - 3y) = -4(-9)$

$-4x + 12y = 36$

Now we have the following system:

$-4x + 12y = 36$

$4x - 2y = -6$

Add the two equations together to eliminate $x$:

$(-4x + 12y) + (4x - 2y) = 36 + (-6)$

$10y = 30$

Now, divide by 10 to solve for $y$:

$y = \frac{30}{10}$

$y = 3$

Next, substitute $y = 3$ into the first original equation to solve for $x$:

$x - 3(3) = -9$

$x - 9 = -9$

$x = -9 + 9$

$x = 0$

3. Final Answer

The solution to the system of equations is $x = 0$ and $y = 3$.

$(0, 3)$