解方程组:3x+2y+5z=2x−2y−z=64x+2y−7z=30..

问题描述:

解方程组:

3x+2y+5z=2
x−2y−z=6
4x+2y−7z=30.

3x+2y+5z=2①
x−2y−z=6②
4x+2y−7z=30③

①+②可得:4x+4z=8,方程可以变形为z=2-x,④;
②+③可得:5x-8z=36,⑤;
把④代入⑤可得:5x-8(2-x)=36,
                   5x-16+8x=36,
                        13x=52,
                          x=4;
把x=4代入④可得:z=-2,
把x=4,z=-2代入①可得:12+2y-10=2,
                             2y=0,
                              y=0,
所以这个方程组的解是:
x=4
y=0
z=−2