For the following problems, you need to provide a clear and detailed solution. Work Problem 1 (20 points): Consider the following system of linear equations \left\{\begin{array}{l} 7 x_{1}+x_{2}=9 \\ x_{1}-x_{2}+3

x_{3}=17 \\ 5 x_{1}+x_{3}=11 \end{array}\right. (a) [5 pts] Determine whether (1, 2, 3) is a solution to the given system. (b) [15 pts] Solve the given system using theme thod of elimination.