Question

3x+4y+z=14 x+5y+2z=11 2x+2y-z=3 x-y=7 5x+2y=8 解方程？

Answer 1

3x+4y+z=14 ①
x+5y+2z=11 ②
2x+2y-z=3③
①*2-②
6x+8y+2z-x-5y-2z=28-11
5x+3y=17④
①+③
3x+4y+z-2x-2y-z=14+11
x+2y=25⑤
由⑤得：x=25-2y 代入④
5*(25-2y)+3y=17
125-10y+3y=17
-7y=17-125
-7y=-108
y=6
x=25-2*6=25-12=13
x-y=7①
5x+2y=8②
由①得：x=7+y 代入②
5*(7+y)+2y=8
35+5y+2y=8
7y=-27
y=-27/7
x+27/7=7
x=7-27/7
x=22/7,6,三代入一：3X+4Y+（2X+2Y-3）=14
整理：5X+6Y=17
因为：5X+2Y=8
所以：4Y=9
Y=2.25
X=0.7
Z=2.9,2,用矩阵,2,