解方程组,求出X,Y,Z的值。
X=1000+06Y+0.7ZY=800+0.05X+0.2ZZ=500+0.1X+0.25Y
X=1000+0.6Y+0.7Z (1)
Y=800+0.05X+0.2Z (2)
Z=500+0.1X+0.25Y (3)
由(1)式得:X-0.6Y-0.7Z=1000 → 10X-6Y-7Z=10000 (4)
由(2)式得:Y-0.05X-0.2Z=800 → 20Y-X-4Z=1600 → -X+20Y-4Z=1600 (5)
由(3)式得:Z-0.1X-0.25Y=500 → 20Z-2X-5Y=1000 → -2X-5Y+20Z=1000 (6)
(4)式+(5)×10可以消去X:10X-6Y-7Z-10X+200Y-40Z=10000+16000 →193Y-47Z=26000 (7)
(4)式×2-(5)可以消去X:-2X+40Y-8Z+2X+5Y-20Z=3200-1000 → →45Y-28Z=2200 (8)
(7)式×45-(8))式×193可以消去Y:
193Y×45-47Z×45-45Y×193+28Z×193=26000×45-2200×193
2115Z=1170000-424600
2115Z=745400
Z=745400÷2115=149080/423
把Z=149080/423代入(8))式:
45Y-28×(149080/423)=2200
45Y=5104840/423
Y=1020968/3807
把Z=149080/423和 Y=1020968/3807代入(4))式:
10X-6×(1020968/3807)-7×(149080/423)=10000
10X=6125808/3807+1043560/423+10000
X=22667689704/16103610=11333829852/8051805
所以,X=11333829852/8051805
Y=1020968/3807
Z=149080/423
你的题目数值肯定有问题,但题目就是这么做的