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受欢迎的代数 >

31(x+y)+2z=21,3x-(y+z)=6,5x+(x+y-z)=38

解答

31 (x + y) + 2 z = 21, 3 x - (y + z) = 6, 5 x + (x + y - z) = 38

解答

x = \frac{862}{13}, y = - \frac{1085}{13}, z = \frac{3593}{13}

求解步骤

31 (x + y) + 2 z = 21 3 x - (y + z) = 6 5 x + (x + y - z) = 38

对于

31 (x + y) + 2 z = 21

将

x

移到一边:

x = \frac{21 - 2 z}{31} - y

替代

x = \frac{21 - 2 z}{31} - y

[3 (\frac{21 - 2 z}{31} - y) - (y + z) = 6 5 (\frac{21 - 2 z}{31} - y) + \frac{21 - 2 z}{31} - y + y - z = 38]

化简

[- 4 y + \frac{63 - 37 z}{31} = 6 \frac{- 43 z + 126}{31} - 5 y = 38]

对于

- 4 y + \frac{63 - 37 z}{31} = 6

将

y

移到一边:

y = - \frac{37 z + 123}{124}

替代

y = - \frac{37 z + 123}{124}

[\frac{- 43 z + 126}{31} - 5 (- \frac{37 z + 123}{124}) = 38]

化简

[\frac{13 z + 1119}{124} = 38]

对于

\frac{13 z + 1119}{124} = 38

将

z

移到一边:

z = \frac{3593}{13}

对于

y = - \frac{37 z + 123}{124}

替代

z = \frac{3593}{13}

y = - \frac{37 \cdot \frac{3593}{13} + 123}{124}

- \frac{37 \cdot \frac{3593}{13} + 123}{124} = - \frac{1085}{13}

y = - \frac{1085}{13}

对于

x = \frac{21 - 2 z}{31} - y

替代

y = - \frac{1085}{13}, z = \frac{3593}{13}

x = \frac{21 - 2 \cdot \frac{3593}{13}}{31} - (- \frac{1085}{13})

\frac{21 - 2 \cdot \frac{3593}{13}}{31} - (- \frac{1085}{13}) = \frac{862}{13}

x = \frac{862}{13}

方程组的解为:

x = \frac{862}{13}, y = - \frac{1085}{13}, z = \frac{3593}{13}

流行的例子

3 x - y = 4, - y + 2 x = 1

y = 2 x - 1, 2 y - x = 7

-2x+2y=-4,3x+3y=-18

- 2 x + 2 y = - 4, 3 x + 3 y = - 18

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

3x-4(y-2)=2,2x+3(y-3)=4

3 x - 4 (y - 2) = 2, 2 x + 3 (y - 3) = 4