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We are given the following system of equations:

\[
\begin{cases}
x - 3y = 2 \\
5x + y = -54
\end{cases}
\]

To solve this using the substitution method, follow these steps:

### Step 1: Solve one equation for one variable
We can start by solving the first equation \( x - 3y = 2 \) for \( x \):

\[
x = 3y + 2
\]

### Step 2: Substitute this expression for \( x \) into the second equation
Substitute \( x = 3y + 2 \) into the second equation \( 5x + y = -54 \):

\[
5(3y + 2) + y = -54
\]

### Step 3: Solve for \( y \)
Now, expand and simplify the equation:

\[
15y + 10 + y = -54
\]
\[
16y + 10 = -54
\]
\[
16y = -64
\]
\[
y = -4
\]

### Step 4: Substitute \( y = -4 \) back into the expression for \( x \)
Substitute \( y = -4 \) into \( x = 3y + 2 \):

\[
x = 3(-4) + 2 = -12 + 2 = -10
\]

### Final Answer:
The solution to the system is \( (x, y) = (-10, -4) \).

Let me know if you would like further details or explanations!

Here are 5 related questions you might find interesting:
1. How would the solution process change if we used elimination instead of substitution?
2. Can you confirm the solution by plugging \( x = -10 \) and \( y = -4 \) back into the original equations?
3. What is the geometric interpretation of solving systems of linear equations?
4. How can substitution be used for non-linear systems of equations?
5. How do you handle systems of equations with more than two variables?

**Tip:** Always double-check your solution by substituting the values of the variables back into both original equations to ensure they satisfy the system.

Solve the following system of equations with the substitution method: { x - 3y = 2, 5x + y = -54 }

Learn how to solve the system of equations x - 3y = 2 and 5x + y = -54 using the substitution method. This problem covers key algebraic concepts, including substitution and solving linear equations. Suitable for students in Grades 8-10.

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