algebra

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Use the method of substitution to solve the system.
xy=1
4x-y+3=0

  • algebra -

    xy = 1,
    4x - y + 3 = 0.

    Solve 1st Eq for x:
    X = 1/y,

    Substitute 1/y for x in EQ2:
    4/y - y + 3 = 0,
    Multiply both sides by -y:
    -4 + y^2 - 3y = 0,
    y^2 - 3y - 4 = 0,
    Factor the trinomial:
    (y + 1) (y - 4) = 0,
    y + 1 = 0,
    y = -1.

    y - 4 = 0,
    y = 4.

    Substitute -1 for y in Eq1:
    x*-1 = 1,
    x = -1.

    Substitute 4 for y in Eq1:
    x * 4 = 1,
    x = 1/4.

    Solution set: (-1 , -1) , (1/4 , 4).

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