2) \( \left\{\begin{array}{c}3 x-4 y+2 z=1 \\ -2 x-3 y+z=2 \\ 5 x-y+z=5 \\ \text { s.1. }\end{array}\right. \)

To solve this system of equations, you can use various methods such as substitution, elimination, or matrix techniques. For instance, by re-arranging the first equation, you can express \(z\) in terms of \(x\) and \(y\), then substitute that into the other equations. Remember to check for any special cases, like parallel planes, which might suggest no solution or infinite solutions! One common mistake is forgetting to simplify equations before substituting them, which can lead to unnecessary complexity. Always double-check your algebra before moving to the next step! Keep your work organized, and you’ll avoid some common pitfalls in solving systems of equations. Happy calculating!