Question

solve the system of equations

4x - 8y = -36
-6x + y = 32

Answer 1

To solve the system of equations

\[
4x - 8y = -36 \quad \text{(1)}
\]
\[
-6x + y = 32 \quad \text{(2)}
\]

we can use the substitution or elimination method. Let's use the elimination method.

First, let's simplify equation (1). We can divide every term by 4:

\[
x - 2y = -9 \quad \text{(3)}
\]

Next, we can express \( y \) from equation (2):

\[
y = 6x + 32 \quad \text{(4)}
\]

Now substitute equation (4) into equation (3):

\[
x - 2(6x + 32) = -9
\]

Expanding that gives:

\[
x - 12x - 64 = -9
\]

Combining like terms:

\[
-11x - 64 = -9
\]

Adding 64 to both sides:

\[
-11x = 55
\]

Dividing by -11:

\[
x = -5
\]

Now substitute \( x = -5 \) back into equation (4) to find \( y \):

\[
y = 6(-5) + 32
\]
\[
y = -30 + 32
\]
\[
y = 2
\]

Thus, the solution to the system of equations is:

\[
\boxed{(-5, 2)}
\]