SOLUTION: Hi there, This is my question: State how many solutions exist for each set of equations and state whether the lines are consistent or inconsistent and independent or dependent:

Question 507375: Hi there,
This is my question: State how many solutions exist for each set of equations and state whether the lines are consistent or inconsistent and independent or dependent:
1) A)6x-2y=2
9x-3y=1
I have made it this far in solving the problem, but do not get what I am doing wrong:
-- 9x-3y=1=>9x=1+3y
-- 6x-2y=2 => 15(1+3y)-2y =2
-- 15+45Y-2y=2
-- 43/43y = -13/43
-- Y = ??
I understand that you must use substitution, for example if it were x+y=9 then it would be x=9-y. However I've only ever done it with just a singe Variable. I do not know what to do since this question has a "9x"... do I add the "9x" to the 6x? creating 15x? I hope you understand and see where I went wrong. Thank you in advance for answering my question.

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
the ratio of the x and y coefficients is the same in both equations

multiplying the 1st eqn by 3/2 gives ___ 9x - 3y = 3

the equations generate 2 parallel lines ___ because the lines never intersect, there is no solution

because the equations are the same on the left side but different on the right, they are inconsistent
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