To solve the equation \(3x + 2y = 12\) for \(x\) and \(y\), we can express one variable in terms of the other. Let's solve for \(y\) in terms of \(x\):

1. Start with the equation:
   \[
   3x + 2y = 12
   \]

2. Subtract \(3x\) from both sides:
   \[
   2y = 12 - 3x
   \]

3. Divide both sides by 2 to solve for \(y\):
   \[
   y = \frac{12 - 3x}{2}
   \]
   \[
   y = 6 - \frac{3x}{2}
   \]

So, the solution in terms of \(x\) is \(y = 6 - \frac{3x}{2}\).

If you'd like to find specific values of \(x\) and \(y\), you can choose a value for \(x\) and substitute it into the equation to solve for \(y\), or vice versa. However, with just one equation, \(x\) and \(y\) are dependent on each other and can have infinitely many solutions.

Would you like details on this process or have any questions?

Here are 5 related questions to consider:
1. How do you solve a system of equations with two variables?
2. What happens if we assign specific values to \(x\) or \(y\) in this equation?
3. How would the graph of this equation look in the coordinate plane?
4. Can we solve this problem using matrix methods?
5. How does substitution compare to elimination in solving systems of equations?

**Tip:** Always check your solution by substituting the values back into the original equation to ensure they satisfy it.

Learn how to solve the linear equation 3x + 2y = 12 with a step-by-step solution, including expressing one variable in terms of another. Explore related questions on systems of equations, graphing, and solving techniques. Suitable for students in Grades 6-8.

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