Решите методом Гаусса систему уравнений: а) x+y+z=1 б)     -2x+7y-4z=1    x-y-z=1            4x-8y+5x=1  -x+y+z=-1        3x+2y-4z=1

[latex] \left \{ {{x+y+z=1} \atop {x-y-z=1}} \atop {-x+y+z=-1}} \right. \\ \left \{ {{x+y+z=1} \atop {2x=2}} \atop {2y+2z=0}} \right. \\ \left \{ {{x+y+z=1} \atop {x=1}} \atop {y=-z}} \right. \\ \left \{ {{x=1} \atop {y}} \atop {-y}} \right. [/latex]где у любое число[latex] \left \{ {{-2x+7y-4z=1}|*-1 \atop {4x-8y+5z=1}} \atop {3x+2y-4z=1} \right. \\ \left \{ {{2x-7y+4z=-1} \atop {4x-8y+5z=1}} \atop {3x+2y-4z=1}} \right. \\ \left \{ {{2x-7y+4z=-1} |*-5\atop {4x-8y+5z=1}}|*4 \atop {5x-5y=0}} \right. \\ \left \{ {{-10x+35y-20z=5} \atop {16x-32y+20z=4}} \atop {5x-5y=0}} \right. \\ \left \{ {{-10x+35y-20z=5} \atop {6x+3y=9}}|*5 \atop {5x-5y=0}}|*3 \right. \\ \left \{ {{-2x+7y-4z=1} \atop {30x+15y=45}} \atop {45x=45}} \right. \\ x=1,y=1,z=1[/latex]