SOLUTION: sove by substitution. indicate whether the system is independent, dependent or inconsistent. 2x - 3y = 12 3y - 2x = -12

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Question 395634: sove by substitution. indicate whether the system is independent, dependent or inconsistent.
2x - 3y = 12
3y - 2x = -12
Found 2 solutions by ewatrrr, stanbon:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

2x - 3y = 12  OR 2x = 12 + 3y

3y - 2x = -12  |substituting for 2x

3y - (12+3y) = -12

       -12 = -12  System is dependent as it has an infinite amount of solutions



2x - 3y = 12 OR  y = (2/3)x - 4

3y - 2x = -12 OR y = (2/3)x - 4  

These are the same line, would be graphed on top of one another

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve by substitution. indicate whether the system is independent, dependent or inconsistent.
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2x - 3y = 12
3y - 2x = -12
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x = (12+3y)/2
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Substitute for "x" and solve for "y":
3y - 2[(12+3y)/2] = -12
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3y -(12+3y) = -12
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3y-12-3y = -12
-12 = -12
0 = 0
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The system is true for all Real Number values of y.
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The system is dependent.
Each equation is a multiple of the other.
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Cheers,
Stan H.