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受欢迎的代数 >

4p+3q-r=8,5p-q+3r=12,6p-7q+4r=18

解答

4 p + 3 q - r = 8, 5 p - q + 3 r = 12, 6 p - 7 q + 4 r = 18

解答

p = \frac{220}{91}, q = - \frac{58}{91}, r = - \frac{22}{91}

求解步骤

4 p + 3 q - r = 8 5 p - q + 3 r = 12 6 p - 7 q + 4 r = 18

对于

4 p + 3 q - r = 8

将

p

移到一边:

p = \frac{8 - 3 q + r}{4}

替代

p = \frac{8 - 3 q + r}{4}

[5 \cdot \frac{8 - 3 q + r}{4} - q + 3 r = 12 6 \cdot \frac{8 - 3 q + r}{4} - 7 q + 4 r = 18]

化简

[\frac{- 19 q + 17 r + 40}{4} = 12 \frac{- 23 q + 11 r + 24}{2} = 18]

对于

\frac{- 19 q + 17 r + 40}{4} = 12

将

q

移到一边:

q = - \frac{- 17 r + 8}{19}

替代

q = - \frac{- 17 r + 8}{19}

[\frac{- 23 ( - \frac{- 17 r + 8}{19} ) + 11 r + 24}{2} = 18]

化简

[\frac{- 91 r + 320}{19} = 18]

对于

\frac{- 91 r + 320}{19} = 18

将

r

移到一边:

r = - \frac{22}{91}

对于

q = - \frac{- 17 r + 8}{19}

替代

r = - \frac{22}{91}

q = - \frac{- 17 ( - \frac{22}{91} ) + 8}{19}

- \frac{- 17 ( - \frac{22}{91} ) + 8}{19} = - \frac{58}{91}

q = - \frac{58}{91}

对于

p = \frac{8 - 3 q + r}{4}

替代

q = - \frac{58}{91}, r = - \frac{22}{91}

p = \frac{8 - 3 ( - \frac{58}{91} ) - \frac{22}{91}}{4}

\frac{8 - 3 ( - \frac{58}{91} ) - \frac{22}{91}}{4} = \frac{220}{91}

p = \frac{220}{91}

方程组的解为:

p = \frac{220}{91}, q = - \frac{58}{91}, r = - \frac{22}{91}

流行的例子

x + y = 20, 0 x - 40 = y

f (x) = 3, x^{4} x = - 1

4x-2y=26,3x-4y=17

4 x - 2 y = 26, 3 x - 4 y = 17

4x+8y=20,-4x+2y=-30

4 x + 8 y = 20, - 4 x + 2 y = - 30

x + y = 4, x - y = 4