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

### System of Equations
1. \( y = 3x + 1 \)
2. \( 2y - x = 12 \)

### Steps for Solving by Substitution

1. **Substitute** \( y = 3x + 1 \) from the first equation into the second equation.

   \[
   2(3x + 1) - x = 12
   \]

2. **Expand and Simplify** the equation.

   \[
   6x + 2 - x = 12
   \]
   \[
   5x + 2 = 12
   \]

3. **Solve for \( x \)** by isolating it.

   \[
   5x = 10
   \]
   \[
   x = 2
   \]

4. **Substitute \( x = 2 \) back into the first equation** to find \( y \).

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

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

Would you like further explanation on any step, or do you have any questions?

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Here are 5 related questions to explore further:

1. How do you solve a system of equations using the elimination method instead of substitution?
2. How can you verify that your solution to a system of equations is correct?
3. What types of systems of equations have no solution, and how can you identify them?
4. Can substitution be used for systems of equations with three variables? How?
5. What are some real-life applications of solving systems of linear equations?

**Tip:** When substituting values, always double-check each substitution step to avoid small calculation errors.

Solve this system of equations by using substitution:

1. y = 3x + 1
2. 2y - x = 12

Step-by-step solution for solving the system of equations y = 3x + 1 and 2y - x = 12 using substitution. This problem illustrates algebraic techniques to isolate variables and solve for unknowns, suitable for students in Grades 8-10.

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