The equation \( 2x + 2.5y + 3z = 256 \) is a linear equation with three variables (\(x\), \(y\), and \(z\)). To find a specific solution, more equations or conditions are needed. However, we can express one variable in terms of the others.

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

\[
2x + 2.5y + 3z = 256
\]

Subtract \( 2x \) and \( 2.5y \) from both sides:

\[
3z = 256 - 2x - 2.5y
\]

Divide by 3 to isolate \( z \):

\[
z = \frac{256 - 2x - 2.5y}{3}
\]

This expresses \( z \) in terms of \( x \) and \( y \). You can choose any values for \( x \) and \( y \), then plug them into this formula to get a corresponding \( z \).

Would you like to see some specific solutions by choosing values for \( x \) and \( y \)? Or do you want more details on how to handle such equations?

### Relative Questions:
1. How do you solve a system of linear equations with multiple variables?
2. What does it mean if a linear system has no solution, one solution, or infinitely many solutions?
3. How can you graphically represent the solutions of a linear equation with three variables?
4. What methods can be used to solve systems of equations, such as substitution or elimination?
5. How does changing the coefficients in a linear equation affect its graph and solutions?

### Tip:
In linear algebra, an equation with fewer equations than variables typically has infinitely many solutions, forming a plane in 3D space if dealing with three variables.

Explore how to solve the linear equation 2x + 2.5y + 3z = 256. This problem focuses on linear algebra concepts, including solving equations with three variables and expressing one variable in terms of others. Suitable for Grades 10-12.

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