We need to solve the system of linear equations for $x$ and $y$: $-4x + 5y = 32$ $-3x + 4y = 25$

1. Problem Description

We need to solve the system of linear equations for $x$ and $y$:

$-4x + 5y = 32$

$-3x + 4y = 25$

2. Solution Steps

We can use the elimination method to solve this system.

Multiply the first equation by 3 and the second equation by 4 to eliminate $x$:

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

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

This gives us:

$-12x + 15y = 96$

$-12x + 16y = 100$

Subtract the first equation from the second equation:

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

$-12x + 16y + 12x - 15y = 4$

$y = 4$

Now substitute $y = 4$ into the first equation:

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

$-4x + 20 = 32$

$-4x = 32 - 20$

$-4x = 12$

$x = \frac{12}{-4}$

$x = -3$

3. Final Answer

$x = -3$ and $y = 4$