To solve the equation $3x + 4y - 6z = -60$, we need more information, as it's currently a single equation with three unknowns. In general, to find the exact values of $x$, $y$, and $z$, we would need two additional independent equations to form a system.

Without that, we can express one variable in terms of the others. For example, we can solve for $z$ in terms of $x$ and $y$:

$-6z = -60 - 3x - 4y$

$z = \frac{60 + 3x + 4y}{6}$

This expresses $z$ in terms of $x$ and $y$. We could do similar rearrangements for $x$ or $y$ if needed.

Would you like to provide more equations, or continue exploring this solution?

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Here are five related questions for further practice:

1. How would you solve for $y$ in terms of $x$ and $z$?
2. What happens if $z = 0$ in the original equation?
3. Can you find integer solutions for $x$, $y$, and $z$ using this equation?
4. How would you graph this equation in three-dimensional space?
5. How does adding another equation change the possible solutions?

Tip: For systems of equations with multiple variables, using substitution or elimination methods can help find exact solutions!