We are given a system of two linear equations with two variables, $x$ and $y$: $-4x - 3y = 23$ $8x - 9y = 29$ We need to solve this system using the elimination method.

1. Problem Description

We are given a system of two linear equations with two variables, $x$ and $y$:

$-4x - 3y = 23$

$8x - 9y = 29$

We need to solve this system using the elimination method.

2. Solution Steps

First, we can multiply the first equation by 2 to make the coefficients of $x$ in both equations additive inverses.

$2(-4x - 3y) = 2(23)$

$-8x - 6y = 46$

Now we have the following system:

$-8x - 6y = 46$

$8x - 9y = 29$

Next, we add the two equations to eliminate $x$:

$(-8x - 6y) + (8x - 9y) = 46 + 29$

$-8x + 8x - 6y - 9y = 75$

$-15y = 75$

Now, we solve for $y$:

$y = \frac{75}{-15}$

$y = -5$

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

$-4x - 3y = 23$

$-4x - 3(-5) = 23$

$-4x + 15 = 23$

$-4x = 23 - 15$

$-4x = 8$

$x = \frac{8}{-4}$

$x = -2$

3. Final Answer

The solution is $x = -2$ and $y = -5$.

Final Answer: $x = -2$, $y = -5$

We can write it as an ordered pair: $(-2, -5)$