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受欢迎的代数 >

2x-y+3z=13,x+2y+z=12,3x-y+z=7

解答

2 x - y + 3 z = 13, x + 2 y + z = 12, 3 x - y + z = 7

解答

x = 2, y = 3, z = 4

求解步骤

2 x - y + 3 z = 13 x + 2 y + z = 12 3 x - y + z = 7

对于

2 x - y + 3 z = 13

将

x

移到一边:

x = \frac{13 + y - 3 z}{2}

替代

x = \frac{13 + y - 3 z}{2}

[\frac{13 + y - 3 z}{2} + 2 y + z = 12 3 \cdot \frac{13 + y - 3 z}{2} - y + z = 7]

化简

[\frac{5 y - z + 13}{2} = 12 \frac{y - 7 z + 39}{2} = 7]

对于

\frac{5 y - z + 13}{2} = 12

将

y

移到一边:

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

替代

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

[\frac{\frac{z + 11}{5} - 7 z + 39}{2} = 7]

化简

[\frac{- 17 z + 103}{5} = 7]

对于

\frac{- 17 z + 103}{5} = 7

将

z

移到一边:

z = 4

对于

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

替代

z = 4

y = \frac{4 + 11}{5}

\frac{4 + 11}{5} = 3

y = 3

对于

x = \frac{13 + y - 3 z}{2}

替代

y = 3, z = 4

x = \frac{13 + 3 - 3 \cdot 4}{2}

\frac{13 + 3 - 3 \cdot 4}{2} = 2

x = 2

方程组的解为:

x = 2, y = 3, z = 4

流行的例子

9x+11y=-14,6x-5y=-34

9 x + 11 y = - 14, 6 x - 5 y = - 34

x + y = 3, 2 x - y = 0

3x+2y=14,5x-2y=2

3 x + 2 y = 14, 5 x - 2 y = 2

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

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

2x+3y=2,-6x+12y=1

2 x + 3 y = 2, - 6 x + 12 y = 1