\( 1 \leftarrow \begin{array}{l}\text { Solve the given system of equations. } \\ \qquad \begin{array}{l}5 x+4 y-5 z=36 \\ 2 x-4 y+2 z=-4 \\ 4 x-3 y+4 z=12\end{array} \\ \text { Select the correct choice below and fill in any answer boxes within your choice. } \\ \text { A. There is one solution. The solution set is }\{(\square), \square)\} \text {. (Simplify your answers.) } \\ \text { B. There are infinitely many solutions. }\end{array} \) ? \( \quad \).

To solve the system of equations, we can use methods like substitution or elimination. If we set this equation up in a matrix form and use the row reduction technique, we would typically aim to achieve reduced row echelon form. After solving this system, we find that there is one unique solution: \( x = 2, y = 1, z = 5 \). Therefore, the correct choice is A. The solution set is { (2, 1, 5) }. As for the importance of equations in real life, think about how engineers and architects use systems of equations to design structures, optimize resources, or create efficient systems. By solving these equations, they can ensure everything fits together seamlessly—just like a well-crafted puzzle!