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受欢迎的代数 >

x-y-2z=0,-2x-6z=1,-x+2y+z=1

解答

x - y - 2 z = 0, - 2 x - 6 z = 1, - x + 2 y + z = 1

解答

x = \frac{1}{4}, y = \frac{3}{4}, z = - \frac{1}{4}

求解步骤

x - y - 2 z = 0 - 2 x - 6 z = 1 - x + 2 y + z = 1

对于

- 2 x - 6 z = 1

将

x

移到一边:

x = - \frac{1 + 6 z}{2}

替代

x = - \frac{1 + 6 z}{2}

[- \frac{1 + 6 z}{2} - y - 2 z = 0 - (- \frac{1 + 6 z}{2}) + 2 y + z = 1]

化简

[- y + \frac{- 1 - 10 z}{2} = 0 2 y + \frac{1 + 8 z}{2} = 1]

对于

- y + \frac{- 1 - 10 z}{2} = 0

将

y

移到一边:

y = \frac{- 10 z - 1}{2}

替代

y = \frac{- 10 z - 1}{2}

[2 \cdot \frac{- 10 z - 1}{2} + \frac{1 + 8 z}{2} = 1]

化简

[\frac{1 - 12 z}{2} - 1 = 1]

对于

\frac{1 - 12 z}{2} - 1 = 1

将

z

移到一边:

z = - \frac{1}{4}

对于

y = \frac{- 10 z - 1}{2}

替代

z = - \frac{1}{4}

y = \frac{- 10 ( - \frac{1}{4} ) - 1}{2}

\frac{- 10 ( - \frac{1}{4} ) - 1}{2} = \frac{3}{4}

y = \frac{3}{4}

对于

x = - \frac{1 + 6 z}{2}

替代

y = \frac{3}{4}, z = - \frac{1}{4}

x = - \frac{1 + 6 ( - \frac{1}{4} )}{2}

- \frac{1 + 6 ( - \frac{1}{4} )}{2} = \frac{1}{4}

x = \frac{1}{4}

方程组的解为:

x = \frac{1}{4}, y = \frac{3}{4}, z = - \frac{1}{4}

流行的例子

12x+16y=18,14x+18y=20

12 x + 16 y = 18, 14 x + 18 y = 20

x - y = 6, x + y = - 7

72x+3y=41,1-4x-1=18

72 x + 3 y = 41, 1 - 4 x - 1 = 18

7.2m=1,5.7r=4,2n=50,x=2

7.2 m = 1, 5.7 r = 4, 2 n = 50, x = 2

-5x+y=18,3x-y=-14

- 5 x + y = 18, 3 x - y = - 14