方程组{X+Y+Z=6{3X-Y+2Z=12{X-Y-3Z=-4{X+Y+Z=6{3X-Y+2Z=12{X-Y-3Z=-4{3X-2Y=-20{2X+15Y=3

Question

方程组{X+Y+Z=6{3X-Y+2Z=12{X-Y-3Z=-4
{X+Y+Z=6
{3X-Y+2Z=12
{X-Y-3Z=-4
{3X-2Y=-20
{2X+15Y=3

Answer 1

第一题：x + y + z = 6 (1)
3x - y + 2z = 12 (2)
x - y - 3z = -4 (3)
(1) + (2)得：4x + 3z = 18 (4)
(1) + (3)得：2x - 2z = 2 (5)
(4) - (5)×2得 7z = 14 解得：z = 2
把z = 2代入（5）得：x = (2 + 2z)/2 = (2 + 2×2)/2 = 3
把 x = 3 z = 2代入（1）得：y = 6 - x - z = 6 - 3 - 2 = 1
所以原方程组的解是 x = 3 ,y = 1,z = 2
第二题：3x - 2y = -20 (1)
2x + 15y = 3 (2)
(1)×2 - (2)×3得：－49y = -49 解得：y = 1
把 y = 1代入（1）得：x = (-20 + 2y )/3 = (-20 + 2×1)/3 = -6
所以,原方程组的解是 x = -6 ,y = 1