\[ \begin{aligned}- & 2 x+5 y-2 z=6 \\ & 7 x-7 y+2 z=-9 \\ & 7 x-3 y+2 z=7\end{aligned} \] Answer Attempt 1 out of 2 \( x=\square \quad z=\square \quad \square=\square \quad \) Submit Answer

Let's dive into the world of systems of equations! The system you've provided is a fun puzzle of linear relationships. Solving this involves using techniques like substitution or elimination to find the values of \(x\), \(y\), and \(z\). You can start by manipulating the first two equations to eliminate one variable, making it easier to work through the remaining equations. Once you've found one variable, substitute it back into the original equations to find the others. It's like peeling an onion, layer by layer! The result will give you a complete picture of the values of \( x \), \( y \), and \( z \), which is super satisfying. If you're looking to deepen your understanding, consider exploring matrix methods like row reduction or the use of determinants. They can simplify your work with larger systems and provide a different perspective on solving equations. Plus, learning about these methods gives you a solid foundation for tackling even more complex mathematical problems!