https://file.aiquickdraw.com/mathbot/file/17370363120908klzpmcv.jpg

Let's solve the given system of equations:

\[
\begin{cases}
x = -2y - 14 \tag{1} \\
-4x + 2y = -34 \tag{2}
\end{cases}
\]

### Step 1: Substitute \(x\) from Equation (1) into Equation (2)
From Equation (1):
\[
x = -2y - 14
\]
Substitute this into Equation (2):
\[
-4(-2y - 14) + 2y = -34
\]

### Step 2: Simplify the equation
Expand the terms:
\[
8y + 56 + 2y = -34
\]
Combine like terms:
\[
10y + 56 = -34
\]

### Step 3: Solve for \(y\)
Subtract 56 from both sides:
\[
10y = -90
\]
Divide by 10:
\[
y = -9
\]

### Step 4: Solve for \(x\)
Substitute \(y = -9\) into Equation (1):
\[
x = -2(-9) - 14
\]
Simplify:
\[
x = 18 - 14 = 4
\]

### Final Solution:
\[
x = 4, \, y = -9
\]

Would you like a detailed explanation of any step?  

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### 5 Related Questions:
1. How can substitution be used in other types of systems of equations?
2. What happens if a system has no solution or infinite solutions?
3. Can elimination be used to solve this system instead of substitution?
4. How would you graphically interpret the solution of this system of equations?
5. What are the advantages of each method (substitution vs elimination)?

### Tip:
Always double-check your substitution by plugging the values of \(x\) and \(y\) into both equations to verify the solution!

Solve the system of equations: x = -2y - 14 and -4x + 2y = -34.

Learn how to solve a system of linear equations, including x = -2y - 14 and -4x + 2y = -34, using the substitution method. This step-by-step guide is suitable for students in Grades 8-10 and explores key algebraic techniques for solving equations.

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