1.5.19 Systems of Algebraic Equations

Condition: the system of equations to lead to an equivalent allowed system, including in a set of permitted unknown \ (x_ {1}, x_ {2}, x_ {3} \). Write out a general solution, find an appropriate basic solution. Restore the system and write down a new general and appropriate basic solution. \ [\ left \ {\ begin {array} {c} 2 x_ {1} +3 x_ {2} +4 x_ {3} +9 x_ {4} +16 x_ {5} = 1 \\ x_ {1} +2 x_ {2} +2 x_} +5 +5 +5 +5 +5 +5 +5 +5 +5 +5 +5 +5 x_ {4} +9 x_ {5} = 1 \\ 3 x_ {1} +3 x_ {2} +5 x_ {3} +11 x_ {4} +20 x_ {5} = 2 {array} \ right. \]