math-matrix equations

I have a problem with the following homework question:
Which product represents the solution to the system: -y + 7x=14
-x + 4y=1

a. | (1/27) (4/27)|
| (7/27) (1/27)|

b. | (-7/3) (4/3) |
| (-1/3) (1/3) |

c. | (7/3) (-4/3) |
| (1/3) (-1/3) |

d. | (-1/27) (-4/27) |
| (-4/27) (-1/27) |

in every answer above, the matrices are multiplied by
|1 |
|14|

I'm totally confused about how they got those answers...I came up with this as a solution: 1/27 mult. by
|4 1 |
|1 7 | mult. by
|14 |
|1 |
i'm not sure what i'm doing wrong...
i really need help with this question. thanks in advance!

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  1. 7 -1 14
    -1 4 1

    divide first row by 7 to get 1 at A11
    +1 -1/7 + 2
    -1 + 4 + 1

    add them to get 0 in A21
    +1 -1/7 + 2
    +0 27/7 + 3

    multiply second row by 7/27 to get 1 in A22
    +1 -1/7 + 2
    +0 + 1 + 7/9

    that means y = 7/9. to get rid of the -1/7 in A12, add 1/7 times row 2 to row 1
    1 0 19/9
    0 1 7/9
    so
    x = 19/9
    y = 7/9

    check
    -y + 7 x = -7/9 +133/9 = 126/9 = 14 check
    -x+4y = -19/9 + 28/9 = 9/9 = 1 check

    I think you may have a typo in the problem statement.

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  2. no, the problem statement is as it is on my sheet.

    do you know how to answer the question how they want it (a, b, c, or d)?

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  3. trying inverse at the same time

    7 -1 14 1 0
    -1 4 1 0 1

    divide first row by 7 to get 1 at A11
    +1 -1/7 + 2 +1/7 0
    -1 + 4 + 1 0 1

    add them to get 0 in A21
    +1 -1/7 + 2 1/7 0
    +0 27/7 + 3 1/7 1

    multiply second row by 7/27 to get 1 in A22
    +1 -1/7 + 2 1/7 0
    +0 + 1 + 7/9 1/27 7/27

    that means y = 7/9. to get rid of the -1/7 in A12, add 1/7 times row 2 to row 1
    1 0 19/9 4/27 1/27
    0 1 7/9 1/27 7/27
    That means the inverse is
    4/27 1/27
    1/27 7/27
    that inverse times the column 14 1
    should solve it
    4/27 1/27 | 14
    1/27 7/27 | 1

    19/9
    7/9
    caramba

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  4. so answer a does it

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  5. but I had to multiply by {14 1} not {1 14}

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  6. In other words, we agree.

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  7. thanks, this question is very strange but your replies are veryvery helpful =)

    much appreciated!

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