We are asked to solve the system of equations: $ \begin{cases} -4x + 3y = -9 \\ 3x - 2y = 8 \end{cases} $ using elimination or any other convenient method.

1. Problem Description

We are asked to solve the system of equations:

$$

\begin{cases}

-4x + 3y = -9 \\

3x - 2y = 8

\end{cases}

$$

using elimination or any other convenient method.

2. Solution Steps

We will use the elimination method. Multiply the first equation by 2 and the second equation by 3 to eliminate $y$.

$2(-4x + 3y) = 2(-9)$

$-8x + 6y = -18$

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

$9x - 6y = 24$

Add the two resulting equations:

$(-8x + 6y) + (9x - 6y) = -18 + 24$

$x = 6$

Substitute $x = 6$ into the first equation:

$-4(6) + 3y = -9$

$-24 + 3y = -9$

$3y = -9 + 24$

$3y = 15$

$y = 5$

Thus, the solution is $x = 6$ and $y = 5$.

3. Final Answer

$(x, y) = (6, 5)$