ｍａｔｈｓ　問題(+10點)

4x+2y+8z=2 ....(1)
-x-y-2z=2.........(2)
-6x-9y-6z=9......(3)

(2)x4:
4(-x-y-2z)=4*2
-4x-4y-8z=8......(4)
(1)+(4):
(4x+2y+8z)+(-4x-4y-8z)=2+8
4x-4x+2y-4y+8z-8z=10
-2y=10
y=-5

(2)x6:
6(-x-y-2z)=6*2
-6x-6y-12z=12.....(5)
(3)-(5):
(-6x-9y-6z)-(-6x-6y-12z)=9-12
-6x+6x-9y+6y-6z+12z=-3
-3y+6z=-3
y-2z=1................(6)
put y=-5 into (6)
-5-2z=1
-2z=6
z=-3
put y=-5 and z=-3 into (1)
4x+2(-5)+8(-3)=2
4x-10-24=2
4x=36
x=9

so x=9 , y=-5 and z=-3

4x + 2y + 8z = 2 ………………..…(1)
– x – y – 2z = 2 ……………………(2)
– 6x – 9y – 6z = 9 …………………(3)

From (1), (2) & (3), we get
2x + y + 4z = 1 ………………....…(4)
– x – y – 2z = 2 ……………………(5)
– 2x – 3y – 2z = 3 …………………(6)

2(5) + (4),
2(– x – y – 2z) + (2x + y + 4z) = 2(2) + 1
– 2x – 2y – 4z + 2x + y + 4z = 4 + 1
– 2y + y = 5
– y = 5
∴ y = – 5

(4) + (6),
2x + y + 4z + (– 2x – 3y – 2z) = 1 + 3
2x + y + 4z – 2x – 3y – 2z = 4
– 2y + 2z = 4
– y + z = 2 …………………..……(7)

Sub y = – 5 into (7), we get
– (– 5) + z = 25
5 + z = 2
∴ z = – 3

Sub y = – 5 and z = – 3 into (5), we get
– x – (– 5) – 2(– 3) = 2
– x + 5 + 6 = 2
– x + 11 = 2
– x = – 9
∴ x = 9


∴ x = 9, y = – 5, z = – 3



希望幫到您！