Question

解方程组：X+Y—Z=6, X+3Y+2Z=1，3X—2Y—Z=4

Answer 1

X+Y—Z=6, (1)X+3Y+2Z=1(2)3X—2Y—Z=4 (3)
先消去Z
(3)-(1) 得
2x-3Y=2;(4)
(3)*2+(2)得
7x-y=9;(5)
将(5)代入（4）
2x-3*(7x-9)=2;
2x-21x+27=2
-19x=-29
x=29/19
y=7*29/19-9
y=(203-171)/19=32/19
x,y 代入（1)
x+y-6=z(1)
61/19-6=z;
z=-53/19;

Answer 2

X=1.Y=2.Z=-1

Answer 3

X+Y-Z-(3X-2Y-Z)=6-4 --> -2X+3Y=2 --> X=(3Y-2)/2
X+Y-Z+(X+3Y+2Z)+(3X-2Y-Z)=6+1+4 --> 5X+2Y=11
5(3Y-2)/2+2Y=11
15Y-10+4Y=22
19Y=32
Y=32/19
X=(3*32/19-2)/2=29/19
Z=X+Y-6=29/19+32/19-6=-53/19