solve for a and b: 47a+31b=63 31a+47b=15​

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solve for a and b: 47a+31b=63
31a+47b=15​

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Eliza 5 days 2021-09-13T15:51:54+00:00 1 Answer 0 views 0

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    2021-09-13T15:53:50+00:00

    Answer:

    47x + 31y = 63 ……………1

    31x + 47y = 15 ……………2

    Multiply equation 1 by 31 and equation 2 by 47, we get

    47 * 31x + 31 * 31y = 63*31 ……………3

    31 * 47x + 47 * 47y = 15*47 ……………4

    Subtraction equation 3 by 4, we get

    (47 * 31x + 31 * 31y) – (31 * 47x + 47 * 47y) = 63*31 – 15*47

    => 47 * 31x + 31 * 31y – 31 * 47x – 47 * 47y = 63*31 – 15*47

    => 31 * 31y – 47 * 47y = 63*31 – 15*47

    => 961y – 2209y = 1953 – 705

    => -1248y = 1248

    => y = -1248/1248

    => y = -1

    From equation 1, we get

    47x + 31 * (-1) = 63

    => 47x – 31 = 63

    => 47x = 63 + 31

    => 47x = 94

    => x = 94/47

    => x = 2

    Hence, x = 2, y = -1

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