You provided one equation:

\[
3x + y = 6
\]

Since it's a single equation with two variables, it represents a line in the coordinate plane rather than a single solution. To find solutions, you'll need another equation or additional information. However, I can express \( y \) in terms of \( x \) or find specific solutions if you provide a value for \( x \).

### Solving for \( y \) in terms of \( x \):

From the equation \( 3x + y = 6 \), solve for \( y \):

\[
y = 6 - 3x
\]

### Example Solutions:

1. If \( x = 0 \):
   \[
   y = 6 - 3(0) = 6
   \]
   Solution: \( (x, y) = (0, 6) \).

2. If \( x = 2 \):
   \[
   y = 6 - 3(2) = 0
   \]
   Solution: \( (x, y) = (2, 0) \).

3. If \( x = -1 \):
   \[
   y = 6 - 3(-1) = 9
   \]
   Solution: \( (x, y) = (-1, 9) \).

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

Here are 5 related questions:

1. What would the graph of \( 3x + y = 6 \) look like?
2. How can you find the x-intercept and y-intercept of the equation?
3. What happens if you multiply the entire equation by a constant?
4. How would you find the slope and y-intercept of this line?
5. What is the significance of the slope in the context of this equation?

**Tip:** When you have only one equation with two variables, think of it as describing a line. Any point on that line is a solution to the equation.

Learn how to solve the linear equation 3x + y = 6 step-by-step. Understand how to express y in terms of x and find specific solutions with examples provided. Suitable for students in Grades 7-9 studying linear equations and the coordinate plane.

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