ax+by=1, bx-ay=a+b find the value of x and y​

Question

ax+by=1, bx-ay=a+b find the value of x and y​

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Adeline 1 month 2021-10-27T03:16:11+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-27T03:17:40+00:00

    Ax+by=a-b

    ax=a-b-by

    x=a-b-by/a←

    bx-ay=a+b

    substituting

    b(a-b-by/a)-ay=a+b

    ab-b²-b²y/a-ay=a+b

    ab-b²-b²y-a²y/a=a+b

    ab-b²-(b²+a²)y=a²+ab

    -(b²+a²)y=a²+ab-ab+b²

    (b²+a²)y=-(a²+b²)

    y=-(a²+b²)/a²+b²

    y=-1←

    substituting value of y

    x=a-b-b(-1)/a

    x=a-b+b/a

    x=a/a

    x=1

    0
    2021-10-27T03:17:49+00:00

    Answer:


    :

    Multiply this equation to b

    abx+b^2(y)=ab-b^2

    bx-ay=a+b

    Multiply it by a

    abx-a^2(y)=a^2+ab

    Solve both equations

    Subtract it

    y(a^2+b^2)=-(a^2+b^2)

    y=-1

    Second equation

    bx-ay=a+b

    bx+a=a+b

    bx=b

    x=1

    So y=-1 and x=1

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