SOLUTION: Hi, can you please help me with this one? The question is: Solve the system of linear equations by the addition method. Then state whether the system is independent, inconsist

Question 19270: Hi, can you please help me with this one?
The question is:
Solve the system of linear equations by the addition method. Then state whether the system is independent, inconsistent or dependent:
1/2x + 1/3y = 1/3
1/6x + 1/3y = 2/9
Thanks!
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
The question is:
Solve the system of linear equations by the addition method. Then state whether the system is independent, inconsistent or dependent:
1/2x + 1/3y = 1/3........multiply throughout with 6..
3x+2y=2............(1)
1/6x + 1/3y = 2/9.......multiply throughout with 18
3x+6y=4............(2)
eqn.(2)-eqn.(1)...4y=2..or...y=2/4=1/2
substituting in (1)...3x+2*1/2=2
3x=2-1=1
x=1/3...
since we got unique solution for x and y ,the equations are consistent and independent
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