To solve the equation \( 6x + 15y = -75 \), let's simplify it first. 

### Step 1: Simplify the equation
We can divide the entire equation by the greatest common divisor (GCD) of the coefficients of \(x\), \(y\), and the constant term. The GCD of 6, 15, and -75 is 3.

Dividing through by 3:

\[
\frac{6x + 15y}{3} = \frac{-75}{3}
\]

This simplifies to:

\[
2x + 5y = -25
\]

### Step 2: Solve for \(x\) or \(y\)
Now, we can solve for one variable in terms of the other. Let's solve for \(x\) in terms of \(y\).

\[
2x = -25 - 5y
\]

\[
x = \frac{-25 - 5y}{2}
\]

This gives the equation \( x = \frac{-25 - 5y}{2} \), where \(x\) is expressed in terms of \(y\). Alternatively, you can solve it for \(y\) in terms of \(x\), or solve it as a system if more information is provided.

Would you like further details on solving this system or graphing the equation?

Here are 5 related questions for exploration:
1. How would you solve for \(y\) in terms of \(x\)?
2. What is the geometric interpretation of this equation?
3. How do we find the intercepts of the equation?
4. What happens when you solve this equation with a second equation for a system of equations?
5. Can this equation be solved using matrices?

**Tip:** Always simplify equations by factoring out common divisors first for easier calculations.

Learn how to simplify and solve the linear equation 6x + 15y = -75. The problem involves algebraic simplification by dividing the equation by the greatest common divisor (GCD) and solving for one variable in terms of another. Ideal for students in Grades 8-10.

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