Question

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

−6x+y=32
(1 point)
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1 answer

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:

\[ (-5, 2) \]