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To solve the given system of equations using the substitution method, let's go through the steps:

### Given System of Equations
1. \( x + 5y = -49 \)
2. \( -3x + y = -13 \)

### Step 1: Solve for \( y \) in terms of \( x \) from the second equation
From the second equation:
\[
-3x + y = -13
\]
Add \( 3x \) to both sides:
\[
y = 3x - 13
\]

### Step 2: Substitute \( y \) in the first equation
Now, substitute \( y = 3x - 13 \) into the first equation:
\[
x + 5(3x - 13) = -49
\]
Expand the equation:
\[
x + 15x - 65 = -49
\]
Combine like terms:
\[
16x - 65 = -49
\]
Add \( 65 \) to both sides:
\[
16x = 16
\]
Now, divide by \( 16 \):
\[
x = 1
\]

### Step 3: Substitute \( x = 1 \) back into the equation for \( y \)
Now, substitute \( x = 1 \) into \( y = 3x - 13 \):
\[
y = 3(1) - 13
\]
\[
y = 3 - 13
\]
\[
y = -10
\]

### Solution
The solution to the system is:
\[
(x, y) = (1, -10)
\]

You can now enter \( x = 1 \) and \( y = -10 \) in the answer fields on your assessment.

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Would you like further details or have any questions about this solution? 

Here are some related questions to explore:
1. How does the substitution method differ from the elimination method?
2. What are other methods to solve a system of linear equations?
3. Why do we isolate one variable in substitution?
4. Can this system of equations be solved graphically? If so, how?
5. How do you interpret the solution to a system of linear equations geometrically?

**Tip:** Always double-check your substitutions in each equation to confirm accuracy in solutions for systems of equations.

Solve the following system of equations with the substitution method:
1. x + 5y = -49
2. -3x + y = -13

Learn how to solve the system of equations x + 5y = -49 and -3x + y = -13 using the substitution method. Step-by-step explanation provided. Suitable for students in Grades 9-11.

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