Thank you for the opportunity to help you with your question!
Hi there. :) Each of those equations in the original system of equations represent lines. When you go through the linear combination method to find a solution to a system of equations and the end result is something that is never true, such as 0=-12, that means that there is no solution to the system of equations and that the lines are parallel. So the answer to this question would be the first option.
Option 2 is invalid because if the two equations were just different forms of the same line, there would be an infinite number of solutions.
Option 3 is invalid because parallel lines can not intersect, and therefore the system of equations can have no solution.
Option 4 would only occur if you used the linear combination method and the end result was something that was always true, such as 0=0 or 5=5 etc. We know this isn't the case because we ended up with 0=-12
Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 27th, 2015
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