1.5.20 Systems of algebraic equations

Condition: Using the Jordan-Gauss method, investigate the compatibility of the system of equations and, if it is consistent, then find its solution. If the system is uncertain, then find two general and corresponding basic solutions. \[ \left\{\begin{array}{c} 3 x_{1}+4 x_{2}+3 x_{3}+10 x_{4}+17 x_{5}=20 \\ 3 x_{1}+5 x_{2}+3 x_{3}+11 x_{4}+19 x_{5}=22 \\ 6 x_{1}+8 x_{2}+x_{3}+15 x_{4}+24 x_{5}=25 \end{array}\right. \]