Question

Solving using elimination (algebra 1)
-4x - 2y = -12
4x + 8y = -24

Answer 1

To solve the system of equations using elimination, we'll first write the equations:

1) \(-4x - 2y = -12\)
2) \(4x + 8y = -24\)

Next, we can manipulate the equations to eliminate one variable. In this case, we can try to eliminate \(x\) by adding both equations together.

First, let's align the equations:

\[
-4x - 2y = -12 \quad \text{(Equation 1)}
\]
\[
4x + 8y = -24 \quad \text{(Equation 2)}
\]

Now, add Equation 1 and Equation 2 together:

\[
(-4x - 2y) + (4x + 8y) = -12 + (-24)
\]

This simplifies to:

\[
(-4x + 4x) + (-2y + 8y) = -36
\]

\[
0x + 6y = -36
\]

Thus, we have:

\[
6y = -36
\]

Now, solve for \(y\):

\[
y = \frac{-36}{6}
\]

\[
y = -6
\]

Now that we have the value of \(y\), we can substitute it back into one of the original equations to solve for \(x\). Let's use Equation 1:

\[
-4x - 2(-6) = -12
\]

This becomes:

\[
-4x + 12 = -12
\]

Now, subtract 12 from both sides:

\[
-4x = -12 - 12
\]

\[
-4x = -24
\]

Now, divide both sides by -4:

\[
x = \frac{-24}{-4}
\]

\[
x = 6
\]

So, the solution to the system of equations is:

\[
x = 6 \quad \text{and} \quad y = -6
\]

In ordered pair form, the solution is \((6, -6)\).