Question

Question
Solve the system of equations.
4x−8y=−36

−6x+y=32
(1 point)
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,
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Answer 1

To solve the system of equations:

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

We can use the substitution or elimination method. Here, we'll use the substitution method.

### Step 1: Solve Equation 2 for \( y \)

From Equation 2, we can express \( y \) in terms of \( x \):

\[
y = 6x + 32
\]

### Step 2: Substitute \( y \) into Equation 1

Now substitute this expression for \( y \) into Equation 1:

\[
4x - 8(6x + 32) = -36
\]

### Step 3: Simplify the equation

Distributing \( -8 \):

\[
4x - 48x - 256 = -36
\]

Combine like terms:

\[
-44x - 256 = -36
\]

### Step 4: Solve for \( x \)

Add 256 to both sides:

\[
-44x = -36 + 256
\]
\[
-44x = 220
\]

Now divide by -44:

\[
x = \frac{220}{-44} = -5
\]

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

Now substitute \( x = -5 \) back into the equation for \( y \):

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

### Step 6: Solution

The solution to the system of equations is:

\[
(x, y) = (-5, 2)
\]

So the final answer is:

\[
(-5, 2)
\]