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受欢迎的代数 >

2x+y=4,3x+z=6,2y+z=7x+y+z

解答

2 x + y = 4, 3 x + z = 6, 2 y + z = 7 x + y + z

解答

x = \frac{4}{9}, y = \frac{28}{9}, z = \frac{14}{3}

求解步骤

2 x + y = 4 3 x + z = 6 2 y + z = 7 x + y + z

对于

2 x + y = 4

将

x

移到一边:

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

替代

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

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

化简

[\frac{3 ( 4 - y )}{2} + z = 6 2 y + z = z + \frac{28 - 5 y}{2}]

对于

\frac{3 ( 4 - y )}{2} + z = 6

将

y

移到一边:

y = \frac{2 z}{3}

替代

y = \frac{2 z}{3}

[2 \cdot \frac{2 z}{3} + z = z + \frac{28 - 5 \cdot \frac{2 z}{3}}{2}]

化简

[\frac{7 z}{3} = \frac{42 - 2 z}{3}]

对于

\frac{7 z}{3} = \frac{42 - 2 z}{3}

将

z

移到一边:

z = \frac{14}{3}

对于

y = \frac{2 z}{3}

替代

z = \frac{14}{3}

y = \frac{2 \cdot \frac{14}{3}}{3}

\frac{2 \cdot \frac{14}{3}}{3} = \frac{28}{9}

y = \frac{28}{9}

对于

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

替代

y = \frac{28}{9}, z = \frac{14}{3}

x = \frac{4 - \frac{28}{9}}{2}

\frac{4 - \frac{28}{9}}{2} = \frac{4}{9}

x = \frac{4}{9}

方程组的解为:

x = \frac{4}{9}, y = \frac{28}{9}, z = \frac{14}{3}

流行的例子

6r-5t=-11,7t-8r=15

6 r - 5 t = - 11, 7 t - 8 r = 15

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

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

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

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

x - y = 1, x - 3 y = - 3

x + y = 5, 2 x - 3 y = 1