解方程组3x-y+2x=20 2x+y-z=40 7x+y+5z=55
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解方程组3x-y+2x=20 2x+y-z=40 7x+y+5z=55
(1)3x-y+2z=20(后项的2x是不是应该是2z呢)
(2) 2x+y-z=40(与(1)相加得(4)
(4)5x+z=60
(3) 7x+y+5z=55(与(2)相减)得(5)
(5)5x+6z=15(与(4)相减)
5z=-45
z=-9(代入到(4)
5x=69
x=69/5
把x=69/5;z=-9代入到(2)
y=40-2x+z=40-2(69/5)+(-9)=17/5
验算:
(1)左边=3(69/5)-(17/5)+2(-9)=(207-17-90)/5=100/5=20
(2)左边=2(69/5)+17/5-(-9)=(138+17+45)/5=200/5=40
(3)左边=7(69/5)+17/5+5(-9)=(483+17-225)/5=275/5=55
所以,原方程组成立.
(2) 2x+y-z=40(与(1)相加得(4)
(4)5x+z=60
(3) 7x+y+5z=55(与(2)相减)得(5)
(5)5x+6z=15(与(4)相减)
5z=-45
z=-9(代入到(4)
5x=69
x=69/5
把x=69/5;z=-9代入到(2)
y=40-2x+z=40-2(69/5)+(-9)=17/5
验算:
(1)左边=3(69/5)-(17/5)+2(-9)=(207-17-90)/5=100/5=20
(2)左边=2(69/5)+17/5-(-9)=(138+17+45)/5=200/5=40
(3)左边=7(69/5)+17/5+5(-9)=(483+17-225)/5=275/5=55
所以,原方程组成立.
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