The problem is to solve the system of linear equations: $ -4x + 5y = 32 $ $ -3x + 4y = 25 $

1. Problem Description

The problem is to solve the system of linear equations:

$-4x + 5y = 32$

$-3x + 4y = 25$

2. Solution Steps

We can solve this system using the elimination method.

First, multiply the first equation by 3 and the second equation by -4 to eliminate $x$:

$3(-4x + 5y) = 3(32)$

$-12x + 15y = 96$

$-4(-3x + 4y) = -4(25)$

$12x - 16y = -100$

Now add the two new equations:

$(-12x + 15y) + (12x - 16y) = 96 + (-100)$

$-y = -4$

$y = 4$

Substitute $y = 4$ into the first equation:

$-4x + 5(4) = 32$

$-4x + 20 = 32$

$-4x = 32 - 20$

$-4x = 12$

$x = -3$

3. Final Answer

$x = -3$, $y = 4$

The solution is $(-3, 4)$.