We are given the system of two linear equations:

1. \( 3x + 1 = y \)
2. \( 10x - 4y = -8 \)

### Step 1: Substitute \( y \) from the first equation into the second equation
From the first equation, we have:

\[
y = 3x + 1
\]

Now substitute this expression for \( y \) into the second equation:

\[
10x - 4(3x + 1) = -8
\]

### Step 2: Simplify the second equation
Expand the terms in the second equation:

\[
10x - 4(3x + 1) = -8
\]

\[
10x - 12x - 4 = -8
\]

Combine like terms:

\[
-2x - 4 = -8
\]

### Step 3: Solve for \( x \)
Add 4 to both sides:

\[
-2x = -8 + 4
\]

\[
-2x = -4
\]

Now, divide by \(-2\):

\[
x = 2
\]

### Step 4: Solve for \( y \)
Substitute \( x = 2 \) into the first equation \( y = 3x + 1 \):

\[
y = 3(2) + 1 = 6 + 1 = 7
\]

### Solution:
The solution to the system is:
\[
x = 2, \quad y = 7
\]

Would you like more details or have any questions?

Here are five related questions for you:
1. How would the system change if the first equation were \( 3x - 1 = y \)?
2. What happens if both equations were multiplied by a constant factor?
3. Can you find a method to solve the system using matrix algebra?
4. How would you graphically interpret the solution of this system?
5. How can substitution be applied to systems with more complex functions?

**Tip:** Substitution is a powerful method for solving systems of equations, but elimination can be more efficient for larger systems or equations that involve fractions.

Explore how to solve the system of linear equations 3x + 1 = y and 10x - 4y = -8 using the substitution method. The step-by-step guide simplifies both equations, providing a clear path to finding the values of x and y. Ideal for students in Grades 8-10.

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