Question

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

Answer 1

$left { {{x+y+z=1} atop {x-y-z=1}} atop {-x+y+z=-1}} right. \ left { {{x+y+z=1} atop {2x=2}} atop {2y+2z=0}} right. \ left { {{x+y+z=1} atop {x=1}} atop {y=-z}} right. \ left { {{x=1} atop {y}} atop {-y}} right.$

где у любое число

$left { {{-2x+7y-4z=1}|*-1 atop {4x-8y+5z=1}} atop {3x+2y-4z=1} right. \ left { {{2x-7y+4z=-1} atop {4x-8y+5z=1}} atop {3x+2y-4z=1}} right. \ left { {{2x-7y+4z=-1} |*-5atop {4x-8y+5z=1}}|*4 atop {5x-5y=0}} right. \ left { {{-10x+35y-20z=5} atop {16x-32y+20z=4}} atop {5x-5y=0}} right. \ left { {{-10x+35y-20z=5} atop {6x+3y=9}}|*5 atop {5x-5y=0}}|*3 right. \ left { {{-2x+7y-4z=1} atop {30x+15y=45}} atop {45x=45}} right. \ x=1,y=1,z=1$