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6 March, 05:54

A+b=21 b+c=24 c+d=32 d+e=37 e+f=31 f+g=25 g+a=26 find a, b, c, d, e, f, g,

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  1. 6 March, 06:24
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    a = 12

    b = 9

    c = 15

    d = 17

    e = 20

    f = 11

    g = 14

    Step-by-step explanation:

    Given that

    (a + b) = 21 ... (1)

    (b + c) = 24 ... (2)

    (c + d) = 32 ... (3)

    (d + e) = 37 ... (4)

    (e + f) = 31 ... (5)

    (f + g) = 25 ... (6)

    (g + a) = 26 ... (7)

    Hence, adding all the equations we get, 2 (a + b + c + d + e + f + g) = 196

    ⇒ (a + b + c + d + e + f + g) = 98 ... (8)

    Adding equations (2), (4) and (6), we get (b + c + d + e + f + g) = 86.

    Therefore, from equation (8), we get a = 98 - 86 = 12 (Answer)

    Adding equations (3), (5), and (7) we get,

    a + c + d + e + f + g = 89

    Hence, from equation (8), we have b = 98 - 89 = 9 (Answer)

    Similarly, adding equations (1), (4), and (6) we get,

    a + b + d + e + f + g = 83,

    Hence, c = 98 - 83 = 15 (Answer)

    Now, adding equations (2), (5) and (7), we get

    a + b + c + e + f + g = 81. Hence, d = 98 - 81 = 17 (Answer)

    Adding equations (1), (3), and (6)

    a + b + c + d + f + g = 78. Hence e = 98 - 78 = 20 (Answer)

    Adding equations (2), (4), and (7)

    a + b + c + d + e + g = 87. Hence f = 98 - 87 = 11 (Answer)

    Adding equations (1), (3), and (5)

    a + b + c + d + e + f = 84. Hence g = 98 - 84 = 14 (Answer)
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