Question

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 ?

Answer 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.

Answer 2

note the determinant of

2 1
6 3

is 6 - 6 = 0

therefore the solutions using Cramer's Rule are undefined

Answer 3

thank you guys :)

Answer 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)