Question

解三元一次方程 x-y-z=-1 3x+5y+7z=11 4x-y+2z=-1

Answer 1

解 x-y-z=-1与4x-y+2z=-1相减得 3x+3z=0 所以 x=-z
把x-y-z=-1左右相乘以5，得 5x-5y-5z=-5
然后5x-5y-5z=-5与3x+5y+7z=11相加得 8x+2z=6 所以4x+z=3
把x=-z代入4x+z=3得 -4z+z=3 -3z=3 z=-1
把z=-1代入x=-z得 x=1
把x=1 z=-1代入x-y-z=-1得 y=3
所以 x=1 y=3 z=-1

Answer 2

x=-1+y+z, 3(-1+y+z)+5y+7z=11,y=(7-5z)/4 ,4(-1+y+z)-(7-5z)/4+2z=-1 z=3 y=-2 x=2

Answer 3

x-y-z=-1
3x+5y+7z=11
4x-y+2z=-1

x-y=-1+z
z=x-y+1

3x+5y+7(x-y+1)=11
4x-y+2(x-y+1)=-1

3x+5y+7x-7y+7=11
4x-y+2x-2y+2=-1

10x-2y=4
6x-3y=-3

30x-6y=12
30x-15y=-15

9y=27
y=3

6x-3*3=-3
6x-9=-3
x=1

z=1-3+1=-1