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12 November, 05:17

For the following system use the second equation to make a substitution for y in the first equation 2x+y=5 y+3=2x

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  1. 12 November, 08:15
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    1. Substitution: x = y + 10

    3x + 2y - 5 = 0

    3 (y + 10) + 2y = 5

    3y + 2y = 5 - 30

    5y = - 25

    y = - 5 (answer)

    2. Replace x with 2y - 8 in the first equation.

    2y + 5y = 18

    7y = 18

    Simplest form: 7y - 18 = 0, or (c) (answer)

    3.

    q = 1 - 2p

    3p + q + 1 = 0

    q = - 1 - 3p

    1 - 2p = - 1 - 3p

    p = - 2

    Substitute:

    -1 - 3 (-2) = - 1 + 6 = q = 5

    Solution set:

    { (-2,5) }, or (a) (answer)

    4.

    y = 5x - 4

    3x + 5x - 4 = 1, or (a) (answer)

    5.

    y = x + 1

    2x + x + 1 = 7

    3x = 6

    x = 2

    y = 1 + 2 = 3

    Now replace x with 2 and y with 3 in all of the answers and see which one doesn't work.

    a: 7 - 4 - 2 = 1 this works

    b: 4 + 2 + 1 = 7 this works

    c: 2 (4) + 3 = 7 8 + 3 = 11, not 7

    (c) would not be the result of the system. (answer)

    6.

    x = y - 3

    3 (y - 3) + 2y = 7, or (b) (answer)
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