The problem is to solve the system of linear equations: $-4x + 3y = -9$ $3x - 2y = 8$

1. Problem Description

The problem is to solve the system of linear equations:

$-4x + 3y = -9$

$3x - 2y = 8$

2. Solution Steps

We can use the elimination method. To eliminate $x$, we multiply the first equation by 3 and the second equation by 4:

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

$4(3x - 2y) = 4(8)$

This simplifies to:

$-12x + 9y = -27$

$12x - 8y = 32$

Now, add the two equations:

$(-12x + 9y) + (12x - 8y) = -27 + 32$

$-12x + 12x + 9y - 8y = 5$

$y = 5$

Now that we have $y$, substitute it into either of the original equations to solve for $x$. We can use the second equation:

$3x - 2y = 8$

$3x - 2(5) = 8$

$3x - 10 = 8$

$3x = 18$

$x = 6$

So the solution is $x=6$ and $y=5$.

3. Final Answer

(6, 5)