The equation \( x + y = 6 \) represents a linear equation with two variables, \( x \) and \( y \). This equation has infinitely many solutions, as each pair \((x, y)\) that satisfies the equation is a solution. Here are a few possible pairs:

1. If \( x = 0 \), then \( y = 6 \) (since \( 0 + y = 6 \)).
2. If \( x = 2 \), then \( y = 4 \) (since \( 2 + y = 6 \)).
3. If \( x = 3 \), then \( y = 3 \) (since \( 3 + y = 6 \)).
4. If \( x = 4 \), then \( y = 2 \) (since \( 4 + y = 6 \)).
5. If \( x = 6 \), then \( y = 0 \) (since \( 6 + y = 6 \)).

In general, for any value of \( x \), you can find \( y \) by rearranging the equation to \( y = 6 - x \). This linear equation forms a straight line on a graph where all the points \((x, y)\) are solutions to the equation.

Would you like more details or have any questions about this? 

Here are some related questions:

1. How would the graph of the equation \( x + y = 6 \) look like?
2. What is the slope and y-intercept of the line represented by the equation \( x + y = 6 \)?
3. How can this equation be used to find the point of intersection with another line?
4. What happens to the equation if we introduce another equation, like \( 2x + y = 8 \)?
5. How do you solve this equation if \( x \) and \( y \) must be integers?

**Tip:** To find solutions to equations with two variables, you can isolate one variable and express it in terms of the other, making it easier to generate solution pairs or plot the equation on a graph.

Explore how to solve the linear equation x + y = 6 with detailed examples and explanations. Learn about linear equations, graphing, and finding solutions. Suitable for Grades 6-8.

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