To determine the value of [tex]\( x - y \)[/tex] given the system of equations:
[tex]\[
\begin{cases}
4x + 5y = 9 \quad \text{(Equation 1)} \\
3x - 4y = -32 \quad \text{(Equation 2)}
\end{cases}
\][/tex]
we need to solve for [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
### Step 1: Solve for [tex]\( x \)[/tex] and [tex]\( y \)[/tex]
First, we solve the system of linear equations. The solution method typically involves either substitution, elimination, or matrix operations. Upon solving these equations, the values we obtain are:
[tex]\[ x = -4 \][/tex]
[tex]\[ y = 5 \][/tex]
### Step 2: Calculate [tex]\( x - y \)[/tex]
Now that we have the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex], we can calculate [tex]\( x - y \)[/tex]:
[tex]\[ x - y = -4 - 5 = -9 \][/tex]
### Conclusion
Thus, the value of [tex]\( x - y \)[/tex] is:
[tex]\[
\boxed{-9}
\][/tex]
