To solve the equation \( 3x + 2y - 10 = 0 \) for \( x \) and \( y \), you need either another equation or a specific value for one of the variables. However, you can express \( y \) in terms of \( x \) or \( x \) in terms of \( y \). 

Let's solve for \( y \) in terms of \( x \):

\[
3x + 2y - 10 = 0
\]

Add 10 to both sides:

\[
3x + 2y = 10
\]

Now, solve for \( y \):

\[
2y = 10 - 3x
\]

\[
y = \frac{10 - 3x}{2}
\]

So, \( y \) in terms of \( x \) is:

\[
y = 5 - \frac{3x}{2}
\]

Alternatively, if you want to solve for \( x \) in terms of \( y \):

\[
3x = 10 - 2y
\]

\[
x = \frac{10 - 2y}{3}
\]

So, \( x \) in terms of \( y \) is:

\[
x = \frac{10 - 2y}{3}
\]

To find specific values for \( x \) and \( y \), you'd need another equation or a value for one of the variables.

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

Here are some related questions:
1. What happens if we assign specific values to \( x \) or \( y \)?
2. How can we graph the equation \( 3x + 2y - 10 = 0 \)?
3. What is the slope of the line represented by this equation?
4. How do we find the intercepts of this equation with the axes?
5. Can we solve this equation using matrix methods?
6. How does this equation change if we add a constant to it?
7. What is the meaning of this equation in a real-world context?
8. How do we determine if a specific point lies on the line defined by this equation?

**Tip:** When dealing with linear equations in two variables, try to express one variable in terms of the other if you only have one equation.

Learn how to solve the linear equation 3x + 2y - 10 = 0 for x and y with step-by-step solutions and explanations. Explore how to express y in terms of x and x in terms of y. Suitable for Grades 7-9 students and anyone interested in solving linear equations.

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