Algebra

y =1/4x - 4 : y = -7/4x + 4

I need help with this one...has to be solved by elimination. Thanks

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  1. multiply 1st eqn by 7

    add to 2nd eqn to eliminate x

    solve for y , then substitute back to find x

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  2. y = y

    1 / 4 x - 4 = - 7 / 4 x + 4

    Add 7 / 4 x to both sides

    1 / 4 x - 4 + 7 / 4 x = - 7 / 4 x + 4 + 7 / 4 x

    8 / 4 x - 4 = 4

    2 x - 4 = 4

    Add 4 to both sides

    2 x - 4 + 4 = 4 + 4

    2 x = 8

    Divide both sides by 2

    x = 8 / 2

    x = 4

    Replace this value in equation for y.

    y = 1 / 4 x - 4 = x / 4 - 4 = 4 / 4 - 4 = 1 - 4 = - 3

    OR

    y = - 7 / 4 x + 4 = - 7 ∙ x / 4 + 4 = - 7 ∙ 4 / 4 + 4 = - 7 + 4 = - 3

    Solution:

    x = 4 , y = - 3

    You can write this as:

    ( 4 , - 3 )

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  3. -x/4 + y = -4. Standard form.
    Multiply both sides by 4:
    Eq1: -x + 4y = -16.

    7x/4 + y = 4.
    Multiply both sides by 4:
    Eq2: 7x + 4y = 16.

    Multiply Eq1 by -1 and add Eq1 and Eq2:
    x - 4y = 16
    7x + 4y = 16
    Sum: 8x = 32
    X = 4.
    In Eq1, replace X with 4 and solve for Y:
    -4 + 4y = -16.
    Y = -3.

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