To solve the system of equations using the substitution method, follow these steps:

1. **Equations:**
   \[
   x + y = 4 \tag{1}
   \]
   \[
   y = 3x \tag{2}
   \]

2. **Substitute** \( y = 3x \) from equation (2) into equation (1):

   \[
   x + (3x) = 4
   \]
   Simplify:
   \[
   4x = 4
   \]

3. **Solve for** \( x \):
   \[
   x = \frac{4}{4} = 1
   \]

4. **Substitute** \( x = 1 \) into equation (2) to find \( y \):
   \[
   y = 3(1) = 3
   \]

5. **Solution**: 
   The solution to the system of equations is:
   \[
   x = 1, \quad y = 3
   \]

Would you like more details or have any questions?

### Related questions:
1. What if \( y = 2x \) instead of \( y = 3x \)?
2. How does substitution compare to the elimination method?
3. Can the system of equations be solved graphically?
4. What is the general approach for solving nonlinear systems using substitution?
5. How do you verify the solution of a system of equations?

**Tip:** Always check your solution by substituting the values of \( x \) and \( y \) back into the original equations to ensure accuracy!

x + y = 4 and y = 3x using substitution method

Learn how to solve the system of linear equations x + y = 4 and y = 3x using the substitution method. This step-by-step guide covers key algebraic concepts suitable for students in Grades 7-9.

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