https://file.aiquickdraw.com/mathbot/file/17267521409067la64iyx.jpg

The system of equations provided is:

\[
\begin{cases}
-4x - 2y = -12 \\
4x + 8y = -24
\end{cases}
\]

To solve this system using the method of elimination, let's follow these steps:

### Step 1: Add the two equations
Notice that the coefficients of \(x\) in both equations are opposites: \(-4x\) in the first equation and \(4x\) in the second. This allows us to eliminate \(x\) by adding the two equations:

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

Simplifying:

\[
0x + ( -2y + 8y ) = -12 - 24
\]
\[
6y = -36
\]

### Step 2: Solve for \(y\)
Now, solve for \(y\):

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

### Step 3: Substitute \(y = -6\) into one of the original equations
We can substitute \(y = -6\) into either equation to solve for \(x\). Let's use the first equation:

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

Subtract 12 from both sides:

\[
-4x = -24
\]

Solve for \(x\):

\[
x = \frac{-24}{-4} = 6
\]

### Solution:
The solution to the system is \(x = 6\) and \(y = -6\).

Would you like further details or have any other questions?

Here are 5 related questions to explore:
1. How do you solve systems of equations using substitution?
2. What are the graphical interpretations of solving systems of equations?
3. Can you solve this system by substitution and confirm the same result?
4. How would the solution differ if one of the equations had a different slope?
5. How does the elimination method work for systems with more variables?

**Tip:** Always double-check your solution by substituting the values back into the original equations to ensure correctness!

Solve the system of equations by elimination: -4x - 2y = -12 and 4x + 8y = -24.

This solution demonstrates how to solve the system of equations -4x - 2y = -12 and 4x + 8y = -24 using the elimination method. Key algebraic concepts like elimination, basic algebraic operations, and properties of equality are covered. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation