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Question 394785: How might you interpret the solution of a system of linear equations based on the corresponding graph of the system?
Thanks so much for the help
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
The point where the lines intersect is the solution, because the coordinates of that point will satisfy (read: make true) both of your equations. You need to determine, by inspection of the graph, what the coordinates of that point are and report your answer as an ordered pair, (x,y), using those coordinates. To check your answer, you should substitute this set of coordinates into each of your original equations and verify that you have a true statement for each of the equations.
If both lines graph to the same line, then the solution set is infinite, i.e. every ordered pair that satisfies one equation will satisfy the other. If the lines are parallel, then the solution set is empty.
A consistent system has at least one solution.
An inconsistent system has no solutions.
An independent system has exactly one solution.
A dependent system has infinitely many solutions.
Therefore a system can be either consistent and independent, consistent and dependent, or inconsistent.
John
My calculator said it, I believe it, that settles it
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