pre - CALCULUS

Use Cramer's rule to determine if the system is inconsistent system or contains dependent equations.

2x + y = 8
6x + 3y = 24

A. system is inconsistent
B. system contains dependent equations

b ?

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  1. Yes it's B, since it can be seen clearly that the simplified version of the second equation is equal to the first equation.

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  2. note the determinant of

    2 1
    6 3

    is 6 - 6 = 0

    therefore the solutions using Cramer's Rule are undefined

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  3. thank you guys :)

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  4. the solution would be:

    ( det 8 1 det 2 8
    24 3 6 24
    _____ ______
    det 2 1 2 1
    6 3 , 6 3 )

    which is (0/0, 0/0) The zero in the denominator indicates that the system can not be solved using cramer's rule and is therefore not consistent and independent.

    I have not read this but would conjecture that The zeros in the numerator indicate
    that the system is consistent and dependent.

    ( If it were an inconsistent system, we would expect that both numerators would be non-zero, and not equal to each other)

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