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Let's solve the system of linear equations using the substitution method.

The system is:

\[
\begin{aligned}
x + y &= -4 \quad \text{(Equation 1)} \\
5x + 5y &= -20 \quad \text{(Equation 2)}
\end{aligned}
\]

### Step 1: Solve for one variable in one equation.
From Equation 1, we can solve for \(y\) in terms of \(x\):

\[
y = -4 - x
\]

### Step 2: Substitute this expression for \(y\) into Equation 2.
Substitute \(y = -4 - x\) into Equation 2:

\[
5x + 5(-4 - x) = -20
\]

Now, simplify:

\[
5x - 20 - 5x = -20
\]

\[
-20 = -20
\]

### Step 3: Analyze the result.
The result \(-20 = -20\) is always true, which means the two equations are dependent and represent the same line.

### Conclusion:
Since the system results in a true statement and the two equations are essentially the same, **there are infinitely many solutions**. The two lines are coincident (the same line), meaning every point on one line is also on the other line.

So, the correct answer is: **Infinite number of solutions**.

Would you like more details or have any questions?

Here are five related questions you might want to explore:
1. How can we use the elimination method for solving this system?
2. What are coincident lines, and how do they relate to system solutions?
3. How do you determine whether a system has no solution using substitution?
4. Can substitution always be used to solve any system of equations?
5. How would the solution process change if the second equation was \(5x + 5y = -10\)?

**Tip**: When both equations simplify to the same form, it usually indicates infinite solutions or no solutions, depending on whether the equations are consistent.

Use the method of substitution to solve the system of linear equations: x + y = -4, 5x + 5y = -20.

Learn how to solve the system of equations using substitution for x + y = -4 and 5x + 5y = -20. This problem explores algebraic concepts like dependent systems and the substitution method, and is suitable for students in Grades 8-10.

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