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受欢迎的代数 >

x+2y+5z=23,3x+y+4z=26,6x+y+7z=47

解答

x + 2 y + 5 z = 23, 3 x + y + 4 z = 26, 6 x + y + 7 z = 47

解答

x = 4, y = 2, z = 3

求解步骤

x + 2 y + 5 z = 23 3 x + y + 4 z = 26 6 x + y + 7 z = 47

对于

x + 2 y + 5 z = 23

将

x

移到一边:

x = 23 - 2 y - 5 z

替代

x = 23 - 2 y - 5 z

[3 (23 - 2 y - 5 z) + y + 4 z = 26 6 (23 - 2 y - 5 z) + y + 7 z = 47]

化简

[- 5 y - 11 z + 69 = 26 - 11 y - 23 z + 138 = 47]

对于

- 5 y - 11 z + 69 = 26

将

y

移到一边:

y = - \frac{11 z - 43}{5}

替代

y = - \frac{11 z - 43}{5}

[- 11 (- \frac{11 z - 43}{5}) - 23 z + 138 = 47]

化简

[\frac{6 z - 473}{5} + 138 = 47]

对于

\frac{6 z - 473}{5} + 138 = 47

将

z

移到一边:

z = 3

对于

y = - \frac{11 z - 43}{5}

替代

z = 3

y = - \frac{11 \cdot 3 - 43}{5}

- \frac{11 \cdot 3 - 43}{5} = 2

y = 2

对于

x = 23 - 2 y - 5 z

替代

y = 2, z = 3

x = 23 - 2 \cdot 2 - 5 \cdot 3

23 - 2 \cdot 2 - 5 \cdot 3 = 4

x = 4

方程组的解为:

x = 4, y = 2, z = 3

流行的例子

x + y = 7, 2 x - 3 y = 9

2x-3/4 y=3,5x=2y+7

2 x - \frac{3}{4} y = 3, 5 x = 2 y + 7

2x+4=6,y+4=3x-2

2 x + 4 = 6, y + 4 = 3 x - 2

0x^2-31x=3,y=75

0 x^{2} - 31 x = 3, y = 75

x = 3, y = 7