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受欢迎的代数 >

2x+y+4z=12,8x-3y+2z=23,4x+11y-z=33

解答

2 x + y + 4 z = 12, 8 x - 3 y + 2 z = 23, 4 x + 11 y - z = 33

解答

x = \frac{47}{14}, y = \frac{13}{7}, z = \frac{6}{7}

求解步骤

2 x + y + 4 z = 12 8 x - 3 y + 2 z = 23 4 x + 11 y - z = 33

对于

2 x + y + 4 z = 12

将

x

移到一边:

x = \frac{12 - y - 4 z}{2}

替代

x = \frac{12 - y - 4 z}{2}

[8 \cdot \frac{12 - y - 4 z}{2} - 3 y + 2 z = 23 4 \cdot \frac{12 - y - 4 z}{2} + 11 y - z = 33]

化简

[- 7 y - 14 z + 48 = 23 9 y - 9 z + 24 = 33]

对于

- 7 y - 14 z + 48 = 23

将

y

移到一边:

y = - \frac{14 z - 25}{7}

替代

y = - \frac{14 z - 25}{7}

[9 (- \frac{14 z - 25}{7}) - 9 z + 24 = 33]

化简

[\frac{- 189 z + 225}{7} + 24 = 33]

对于

\frac{- 189 z + 225}{7} + 24 = 33

将

z

移到一边:

z = \frac{6}{7}

对于

y = - \frac{14 z - 25}{7}

替代

z = \frac{6}{7}

y = - \frac{14 \cdot \frac{6}{7} - 25}{7}

- \frac{14 \cdot \frac{6}{7} - 25}{7} = \frac{13}{7}

y = \frac{13}{7}

对于

x = \frac{12 - y - 4 z}{2}

替代

y = \frac{13}{7}, z = \frac{6}{7}

x = \frac{12 - \frac{13}{7} - 4 \cdot \frac{6}{7}}{2}

\frac{12 - \frac{13}{7} - 4 \cdot \frac{6}{7}}{2} = \frac{47}{14}

x = \frac{47}{14}

方程组的解为:

x = \frac{47}{14}, y = \frac{13}{7}, z = \frac{6}{7}

流行的例子

x/2+y/3 =2,*x/4+y/2 =2

\frac{x}{2} + \frac{y}{3} = 2, \cdot \frac{x}{4} + \frac{y}{2} = 2

3x+y=-17,5x+2y=-29

3 x + y = - 17, 5 x + 2 y = - 29

3x-2y=5,((2x))/3+y/2 =-7/9

3 x - 2 y = 5, \frac{( 2 x )}{3} + \frac{y}{2} = - \frac{7}{9}

5x-3y=-5,2x+4y=24

5 x - 3 y = - 5, 2 x + 4 y = 24

2x-y=20,2x+y=48

2 x - y = 20, 2 x + y = 48