Independent? Inconsistent? or Dependent?

Question

Determine whether the system of equations is consistent or inconsistent. If the system is consistent, determine whether the equations are dependent or independent.

 

3x/2 - y/3 = -18

 

 

3x/4 + 2y/9 = -9

 

Independent?

Inconsistent? 

Dependent?

Answer 1

3x/2 - y/3 = -18   Equation A
3x/4 + 2y/9 = -9  Equation B

 

Multiplying A by 24 and B by 36, we get

Equation A':   36x + 8y = -432

Equation B':   27x -  8y = -324

_______________________________

                     63x         = -756

                         x         = - 12

 

Substituting into Equation A'   36(-12) + 8 y = -432

8y = 0 

 

SOLUTION: (-12, 0).  not inconsistent, not dependent.