To solve the equation \(2.5x + 10y - 6y = 15 - 21.5\), we first simplify both sides.

First, combine the like terms on the left side:
\[ 2.5x + 4y = 15 - 21.5 \]

Next, simplify the right side:
\[ 2.5x + 4y = -6.5 \]

This is a linear equation in terms of \(x\) and \(y\). If you need a particular solution, you can solve for one variable in terms of the other. Let's solve for \(x\) in terms of \(y\):

\[ 2.5x = -6.5 - 4y \]
\[ x = \frac{-6.5 - 4y}{2.5} \]

Simplifying further:
\[ x = -2.6 - 1.6y \]

So, \( x = -2.6 - 1.6y \).

If you need a particular solution for \(x\) and \(y\), we can solve for \(y\) in terms of \(x\) instead:

\[ 4y = -6.5 - 2.5x \]
\[ y = \frac{-6.5 - 2.5x}{4} \]

Simplifying further:
\[ y = -1.625 - 0.625x \]

So, \( y = -1.625 - 0.625x \).

Would you like more details or have any questions? Here are some additional questions you might want to explore:

1. How do we graph the equation \(2.5x + 4y = -6.5\)?
2. What are the intercepts of the equation \(2.5x + 4y = -6.5\)?
3. How do we solve a system of linear equations?
4. Can you provide more examples of solving linear equations?
5. What is the geometric interpretation of the equation \(2.5x + 4y = -6.5\)?

**Tip:** When solving linear equations, always aim to simplify the equation by combining like terms and isolating the variable of interest.

Learn how to solve the linear equation 2.5x + 10y - 6y = 15 - 21.5 step-by-step. This problem involves combining like terms and isolating variables to find solutions for both x and y. Suitable for high school students.

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