KutaSoftware: Algebra 1- System Of Equations Elimination Part 1 - Free Printable

Let's solve the system of equations using the elimination method, as shown in your image. The goal is to eliminate one variable by adding or subtracting the equations.

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Given System:

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

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Step 1: Add the two equations

We add equation (1) and equation (2):

$$
\begin{align*}
(-4x - 2y) + (4x + 8y) &= -12 + (-24) \\
(-4x + 4x) + (-2y + 8y) &= -36 \\
0x + 6y &= -36
\end{align*}
$$

So,
$$
6y = -36
$$

Now divide both sides by 6:
$$
y = -6
$$

✔ So, we found $ y = -6 $

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Step 2: Substitute $ y = -6 $ into one of the original equations

Let’s use equation (1):
$$
-4x - 2y = -12
$$

Substitute $ y = -6 $:
$$
-4x - 2(-6) = -12 \\
-4x + 12 = -12
$$

Now solve for $ x $:
$$
-4x = -12 - 12 \\
-4x = -24 \\
x = \frac{-24}{-4} = 6
$$

✔ So, $ x = 6 $

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✔ Final Answer:

$$
x = 6, \quad y = -6
$$

Or as an ordered pair: $ (6, -6) $

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Verification:

Plug $ x = 6 $, $ y = -6 $ into both original equations:

Equation 1:
$-4(6) - 2(-6) = -24 + 12 = -12$ ✔️

Equation 2:
$4(6) + 8(-6) = 24 - 48 = -24$ ✔️

Both are satisfied!

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Summary:

The solution to the system is:
$$
\boxed{(6, -6)}
$$

This matches the work shown in your image — they correctly eliminated $ x $, solved for $ y = -6 $, and then substituted back. Great job!