Question

Solve the system of equations.
4x−8y=−36
−6x+y=32 (1 point)
(, )

Answer 1

To solve the system of equations given by:

1. \( 4x - 8y = -36 \) (Equation 1)
2. \( -6x + y = 32 \) (Equation 2)

Let's start by rewriting both equations.

**Step 1: Isolate \( y \) in Equation 2.**

From Equation 2:
\[
y = 6x + 32
\]

**Step 2: Substitute \( y \) in Equation 1.**

Now, substitute \( y \) from Equation 2 into Equation 1:
\[
4x - 8(6x + 32) = -36
\]

**Step 3: Simplify the equation.**
\[
4x - 48x - 256 = -36
\]
\[
-44x - 256 = -36
\]

**Step 4: Solve for \( x \).**
Add 256 to both sides:
\[
-44x = 220
\]

Now divide by -44:
\[
x = -\frac{220}{44} = -5
\]

**Step 5: Substitute \( x \) back to find \( y \).**

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

**Final Solution:**

The solution to the system of equations is:
\[
(x, y) = (-5, 2)
\]

Thus, the final answer is:
\[
\boxed{(-5, 2)}
\]