Question 199068: Can you please help me to identify and solve this graph to see if its consistent or inconsistent and independent or dependent?
Y = 1/2x 9/2
Y = x + 6
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
In the first place, you have not presented a graph, and even if you had, you cannot "solve" a graph. What you have presented is a system of linear equations. The problem is that you did not render the first equation completely because you left out the sign between the free variable term and the constant term.
However, the simplest process given the form of the equations that you presented involves noticing that you have two expressions in  both of which are equal to  . So, just set the two right hand sides equal to each other giving you a single equation in the single variable which can be solved by ordinary methods. Once you have a value for , you can substitute that value back into either of the original equations and calculate . The solution set is the ordered pair (,).
One of three things can happen when you perform the above process.
1. You will get a single ordered pair solution set.
2. You will end up with an identity statement, i.e. something that is always true regardless of the value of the variables, something like 0 = 0, meaning that there are an infinite number of solutions.
3. You will end up with an absurd result, something like 3 = 0, meaning that there is no solution.
Consistent systems have at least one solution.
Inconsistent systems have no solutions.
Independent systems have exactly one solution.
Dependent systems have an infinite number of solutions.
So for situation 1, the system is consistent and independent.
For situation 2, the system is consistent and dependent.
For situation 3, the system is inconsistent and neither independent nor dependent.
John
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