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受欢迎的代数 >

x+y+z=1,2x-2y+z=3,-3x+y+2z=0

解答

x + y + z = 1, 2 x - 2 y + z = 3, - 3 x + y + 2 z = 0

解答

x = \frac{1}{2}, y = - \frac{1}{2}, z = 1

求解步骤

x + y + z = 1 2 x - 2 y + z = 3 - 3 x + y + 2 z = 0

对于

x + y + z = 1

将

x

移到一边:

x = 1 - y - z

替代

x = 1 - y - z

[2 (1 - y - z) - 2 y + z = 3 - 3 (1 - y - z) + y + 2 z = 0]

化简

[- 4 y - z + 2 = 3 4 y + 5 z - 3 = 0]

对于

- 4 y - z + 2 = 3

将

y

移到一边:

y = - \frac{z + 1}{4}

替代

y = - \frac{z + 1}{4}

[4 (- \frac{z + 1}{4}) + 5 z - 3 = 0]

化简

[4 z - 4 = 0]

对于

4 z - 4 = 0

将

z

移到一边:

z = 1

对于

y = - \frac{z + 1}{4}

替代

z = 1

y = - \frac{1 + 1}{4}

- \frac{1 + 1}{4} = - \frac{1}{2}

y = - \frac{1}{2}

对于

x = 1 - y - z

替代

y = - \frac{1}{2}, z = 1

x = 1 - (- \frac{1}{2}) - 1

化简

x = \frac{1}{2}

方程组的解为:

x = \frac{1}{2}, y = - \frac{1}{2}, z = 1

流行的例子

1/2*x+1/3*y=3,x+1/2*y=5

\frac{1}{2} \cdot x + \frac{1}{3} \cdot y = 3, x + \frac{1}{2} \cdot y = 5

-1/8*x+y= 33/4 ,-1/9*x-1/10*y=-47/30

- \frac{1}{8} \cdot x + y = \frac{33}{4}, - \frac{1}{9} \cdot x - \frac{1}{10} \cdot y = - \frac{47}{30}

16x+11y=15,411x+16y=89

16 x + 11 y = 15, 411 x + 16 y = 89

2x-7y=6,8x-28y=24

2 x - 7 y = 6, 8 x - 28 y = 24

x - y = 7, x + y = 11