The equation \(3x + 2y = 6\) is a linear equation in two variables, \(x\) and \(y\). This type of equation represents a line on a coordinate plane.

Since there are infinitely many points on a line, there are **infinitely many solutions** for this equation. Each solution corresponds to a point \((x, y)\) on the line where the equation holds true.

If we rearrange the equation into slope-intercept form \(y = mx + b\):
\[
3x + 2y = 6 \Rightarrow y = -\frac{3}{2}x + 3
\]
we can see that for every \(x\) value we choose, there is a corresponding \(y\) value that satisfies the equation. This confirms that there is an infinite set of solutions.

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### Related Questions:
1. How do you find specific integer solutions for \(3x + 2y = 6\)?
2. What are the intercepts of the line \(3x + 2y = 6\)?
3. How would you solve a system of two linear equations like \(3x + 2y = 6\) and \(x - y = 1\)?
4. Can a linear equation have no solutions? Under what conditions?
5. How do we determine if a point \((x, y)\) lies on the line \(3x + 2y = 6\)?

### Tip:
When dealing with linear equations, rearranging to slope-intercept form \(y = mx + b\) can help visualize the solutions on a graph.

How many solutions does 3x + 2y = 6 have?

Explore the concept of infinite solutions for the linear equation 3x + 2y = 6, represented as a line on the coordinate plane. This page provides a step-by-step breakdown, explaining how each x-value has a corresponding y-value, making it ideal for Grades 8-10.

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