To solve the equation \(3x + y = 45\), we have two variables (\(x\) and \(y\)) but only one equation. This means there are infinitely many solutions, depending on the values you choose for one of the variables. 

Here are a few ways we can approach this:

1. **Express \(y\) in terms of \(x\)**:
   \[
   y = 45 - 3x
   \]
   This equation shows that for any given value of \(x\), you can calculate the corresponding value of \(y\).

2. **Express \(x\) in terms of \(y\)**:
   \[
   x = \frac{45 - y}{3}
   \]
   Similarly, for any given value of \(y\), you can find the corresponding \(x\).

3. **Find specific solutions**:
   - If \(x = 0\), then \(y = 45\).
   - If \(x = 5\), then \(y = 30\).
   - If \(x = 10\), then \(y = 15\).

4. **Graphical representation**:
   The equation represents a straight line on a coordinate plane. The line will cross the \(y\)-axis at \( (0, 45) \) and the \(x\)-axis at \( (15, 0) \).

Would you like more details, or do you have any specific questions?

Here are some related questions that might interest you:

1. How do you find the slope and intercepts of a linear equation?
2. What happens if we add another equation to form a system of equations?
3. How can we graph this equation on a coordinate plane?
4. What are the real-world applications of linear equations like this one?
5. How can you solve a system of linear equations with more than two variables?

**Tip:** When dealing with linear equations, expressing one variable in terms of the other can help visualize all possible solutions!

Learn how to solve the linear equation 3x + y = 45 by expressing one variable in terms of the other. Explore key algebraic concepts and understand how the equation represents a straight line on a coordinate plane. Suitable for students in Grades 6-8.

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