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受欢迎的代数 >

2x+y-2z=1,x-2y+3z=6,3x-3y-z=5

解答

2 x + y - 2 z = 1, x - 2 y + 3 z = 6, 3 x - 3 y - z = 5

解答

x = \frac{24}{13}, y = - \frac{3}{13}, z = \frac{16}{13}

求解步骤

2 x + y - 2 z = 1 x - 2 y + 3 z = 6 3 x - 3 y - z = 5

对于

2 x + y - 2 z = 1

将

x

移到一边:

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

替代

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

[\frac{1 - y + 2 z}{2} - 2 y + 3 z = 6 3 \cdot \frac{1 - y + 2 z}{2} - 3 y - z = 5]

化简

[\frac{- 5 y + 8 z + 1}{2} = 6 \frac{- 9 y + 4 z + 3}{2} = 5]

对于

\frac{- 5 y + 8 z + 1}{2} = 6

将

y

移到一边:

y = - \frac{- 8 z + 11}{5}

替代

y = - \frac{- 8 z + 11}{5}

[\frac{- 9 ( - \frac{- 8 z + 11}{5} ) + 4 z + 3}{2} = 5]

化简

[\frac{- 26 z + 57}{5} = 5]

对于

\frac{- 26 z + 57}{5} = 5

将

z

移到一边:

z = \frac{16}{13}

对于

y = - \frac{- 8 z + 11}{5}

替代

z = \frac{16}{13}

y = - \frac{- 8 \cdot \frac{16}{13} + 11}{5}

- \frac{- 8 \cdot \frac{16}{13} + 11}{5} = - \frac{3}{13}

y = - \frac{3}{13}

对于

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

替代

y = - \frac{3}{13}, z = \frac{16}{13}

x = \frac{1 - ( - \frac{3}{13} ) + 2 \cdot \frac{16}{13}}{2}

\frac{1 - ( - \frac{3}{13} ) + 2 \cdot \frac{16}{13}}{2} = \frac{24}{13}

x = \frac{24}{13}

方程组的解为:

x = \frac{24}{13}, y = - \frac{3}{13}, z = \frac{16}{13}

流行的例子

x+y/4 =-1,x+y=1

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

2x+3y+4z=3,2x+6y+8z=5,4x+9y-4z=4

2 x + 3 y + 4 z = 3, 2 x + 6 y + 8 z = 5, 4 x + 9 y - 4 z = 4

x+3y=3,2x-y=1.8

x + 3 y = 3, 2 x - y = 1.8

x-y+z=-5,x+2y=4,y-z=-3

x - y + z = - 5, x + 2 y = 4, y - z = - 3

4x-2y=4,3x-2y=5

4 x - 2 y = 4, 3 x - 2 y = 5