六年级三元一次方程组.解下列方程组：(1)5x-3y+z=25x+2y-4z=3-5x+y-z=2(2)x-y-z=-13x5y+7z=114x-y+2z=-1(3)9x-5y+z=-69x+y+4z=3-9x+3y-5z=0(4)x+y=22x+z=-27y+z=13

Question

六年级三元一次方程组.
解下列方程组：
(1)
5x-3y+z=2
5x+2y-4z=3
-5x+y-z=2
(2)
x-y-z=-1
3x_5y+7z=11
4x-y+2z=-1
(3)
9x-5y+z=-6
9x+y+4z=3
-9x+3y-5z=0
(4)
x+y=22
x+z=-27
y+z=13

Answer 1

(1)
5x-3y+z=2 ①
5x+2y-4z=3 ②
-5x+y-z=2 ③
② - ① 得 5y - 5z = 1 ④
① + ③ 得 -2y = 4
所以 y = -2
代入④ 得 z = -11/5
代入① 得 x = -9/25
所以 x = -9/25
y = -2
z = -11/5
(2)
x-y-z=-1 ①
3x-5y+7z=11 ②
4x-y+2z=-1 ③
③ - ① 得 3x + 3z = 0
所以 x = -z ④
将④代入①② 得 y + 2z = 1 ⑤
5y - 4z = -11 ⑥
由⑤* 2 + ⑥ 得 y = -9/7 ,z = 8/7
代入④ 得 x = -8/7
所以 x = -8/7
y = -9/7
z = 8/7
(3)
9x-5y+z=-6 ①
9x+y+4z=3 ②
-9x+3y-5z=0 ③
② - ① 得 6y + 3z = 9
化简 得 2y + z = 3 ④
② + ③ 得 4y - z = 3 ⑤
④ + ⑤ 解得 y = 1
代入④ 得 z = 1
将y = 1,z = 1代入① 得 x = -2/9
所以 x = -2/9
y = 1
z = 1
(4)
x+y=22 ①
x+z=-27 ②
y+z=13 ③
① + ② + ③ 得 x + y + z = 4 ④
④ - ① 得 z = -18
④ - ② 得 y = 31
④ - ③ 得 x = -9
所以 x = -9
y = 31
z = -18