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The solution is where the two lines intersect. So you have no solution precisely if there is no intersection. In what circumstances would you have a situation where two lines in 2space don't intersect? If you have three equations in two variables this represents three lines in 2space. The solution is where the three lines intersect. So you have no solution precisely if there is no intersection, that is no point where all three lines meet. In what circumstances would you have a situation where three lines in 2space don't intersect at a point? What about n lines in 2space? Hope this helps. Hi Ryan, If solving the system by elimination, a system with "no solution" would be one in which eliminating one variable from the system eliminates both variables and results in a statement of equality that is false, such as 2=0. Hope this helps,  


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