Final answer:
The analysis of the given systems without graphing suggests that the equations are likely independent or dependent, with no clear inconsistency directly from the given equations. However, algebraic manipulations or graphic analysis would be required for complete classification.
Step-by-step explanation:
To classify the given systems as independent, dependent, or inconsistent without graphing, we need to analyze each pair of equations to see if they have a solution, and what kind of solution that is (unique or infinite).
Looking at the equations given:
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- 7x - y = 6
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- 7y = 6x + 8
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- 4y = 8
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- y + 7 = 3x
We will go through them pairwise:
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- Equations 7x - y = 6 and 7y = 6x + 8 do not appear to be multiples of each other, suggesting they could be independent, each with their own unique solution set.
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- Equation 4y = 8 simplifies to y = 2. Any other equation involving 'y' could be dependent on this if it becomes an identity when 'y' is replaced with 2, or inconsistent if it leads to a contradiction.
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- Comparing y = 2 with y + 7 = 3x, it appears that the latter is dependent on the former as substituting y = 2 into the second equation yields a valid x value, which would make the system of these two equations dependent.
Hence, without graphing, we can infer that the equations may lead to either independent or dependent solutions, with no clear inconsistencies noted solely from the given information. However, to fully ascertain these classifications, we need to perform algebraic manipulations or graphical analysis, which the question has asked us to avoid.