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受欢迎的代数 >

2x+3y+4z=7,4y=2+5z,3z-2x+6=0

解答

2 x + 3 y + 4 z = 7, 4 y = 2 + 5 z, 3 z - 2 x + 6 = 0

解答

x = \frac{126}{43}, y = \frac{19}{43}, z = - \frac{2}{43}

求解步骤

2 x + 3 y + 4 z = 7 4 y = 2 + 5 z 3 z - 2 x + 6 = 0

对于

4 y = 2 + 5 z

将

y

移到一边:

y = \frac{2 + 5 z}{4}

替代

y = \frac{2 + 5 z}{4}

[3 z - 2 x + 6 = 0 2 x + 3 \cdot \frac{2 + 5 z}{4} + 4 z = 7]

化简

[3 z - 2 x + 6 = 0 2 x + \frac{6 + 31 z}{4} = 7]

对于

3 z - 2 x + 6 = 0

将

z

移到一边:

z = \frac{2 x - 6}{3}

替代

z = \frac{2 x - 6}{3}

[2 x + \frac{6 + 31 \cdot \frac{2 x - 6}{3}}{4} = 7]

化简

[\frac{43 x - 84}{6} = 7]

对于

\frac{43 x - 84}{6} = 7

将

x

移到一边:

x = \frac{126}{43}

对于

z = \frac{2 x - 6}{3}

替代

x = \frac{126}{43}

z = \frac{2 \cdot \frac{126}{43} - 6}{3}

\frac{2 \cdot \frac{126}{43} - 6}{3} = - \frac{2}{43}

z = - \frac{2}{43}

对于

y = \frac{2 + 5 z}{4}

替代

x = \frac{126}{43}, z = - \frac{2}{43}

y = \frac{2 + 5 ( - \frac{2}{43} )}{4}

\frac{2 + 5 ( - \frac{2}{43} )}{4} = \frac{19}{43}

y = \frac{19}{43}

方程组的解为:

x = \frac{126}{43}, y = \frac{19}{43}, z = - \frac{2}{43}

流行的例子

x + y = 14, x - y = 4

2 x - y = 2, 4 x - 4 y = 6

x+y+z=1,6x-y+z=0,-9y+9z=-27

x + y + z = 1, 6 x - y + z = 0, - 9 y + 9 z = - 27

-5x+6y=7,4x+3y=10

- 5 x + 6 y = 7, 4 x + 3 y = 10

x+3y=6,5x-2y=12

x + 3 y = 6, 5 x - 2 y = 12