To solve the system of equations:
-
The first equation is:
\(4x - 8y = -36\)
We can simplify this equation by dividing everything by 4:
\[x - 2y = -9 \quad \text{(Equation 1)}\] -
The second equation is:
\(-6x + y = 32 \quad \text{(Equation 2)}\)
Now, let's solve these equations using the substitution or elimination method. Here, I will use substitution.
From Equation 1, we can express \(x\) in terms of \(y\):
\[x = 2y - 9\]
Now substitute this expression for \(x\) into Equation 2:
\[-6(2y - 9) + y = 32\]
Distributing in the equation:
\[-12y + 54 + y = 32\]
Combine like terms:
\[-11y + 54 = 32\]
Now, isolate \(y\):
\[-11y = 32 - 54\]
\[-11y = -22\]
\[y = 2\]
Now that we have \(y\), substitute \(y = 2\) back into the expression for \(x\):
\[x = 2(2) - 9\]
\[x = 4 - 9\]
\[x = -5\]
Thus, the solution to the system of equations is:
\(\boxed{(-5, 2)}\)