algebra

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The point of intersection of the graphs of the equations of the system
Ax – 4y = 9
4x + By = –1
is (–1, –3). Explain how to find the values of A and B, then find these values.

  • algebra -

    The point (-1,-3) must lie on both curves. Thus
    -A -4*(-3) = 9
    -A +12 = 9
    A = 3
    and
    4*(-1) +B*(-3) = -1
    Solve that for B

  • algebra -

    x = - 1

    y = - 3




    A x – 4 y = 9

    A * ( - 1 ) - 4 * ( - 3 ) = 9

    - A + 12 = 9

    - A = 9 - 12

    - A = -3 Multiply both sides by - 1

    A = 3




    4 x + B y = –1

    4 * ( - 1 ) + B * ( - 3 ) = - 1

    - 4 - 3 B = - 1

    - 3 B = - 1 + 4

    - 3 B = 3 Divide both sides by - 3

    B = 3 / - 3

    B = - 1

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