To solve the equation \( x + 3y = 16 \) for \( x + y \), we need to express \( x \) in terms of \( y \) and then substitute into the second equation.

1. Start with the given equation:
   \[
   x + 3y = 16
   \]
2. Solve for \( x \):
   \[
   x = 16 - 3y
   \]
3. Now, substitute \( x = 16 - 3y \) into the equation \( x + y \):
   \[
   x + y = (16 - 3y) + y
   \]
4. Simplify the equation:
   \[
   x + y = 16 - 3y + y = 16 - 2y
   \]

So, \( x + y = 16 - 2y \).

Do you want more details, or do you have any questions?

### 5 Related Questions:
1. How would you solve \( x + y = 10 \) if given a different linear equation, like \( 2x + 5y = 20 \)?
2. What are the steps for solving a system of linear equations with two variables?
3. How can you use substitution and elimination methods to solve simultaneous equations?
4. What does the solution to a system of linear equations represent geometrically?
5. How do you interpret the solution \( x = 16 - 3y \) in the context of the original equation?

**Tip:** When solving for one variable in terms of another, always isolate the desired variable first and then substitute it into the related equation. This method is known as substitution.

Learn how to solve a linear equation using the substitution method with a step-by-step example. This problem involves finding the values of x and y in the equations x + 3y = 16 and x + y = ... through substitution. Suitable for students in Grades 7-9.

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