please give a brief explanation to why you chose the answer 14. If one is solvin

Question

please give a brief explanation to why you chose the answer

14. If one is solving two linear equations involving three unknowns, what happens? 0 A. Usually there will be no solution, but occasionally there will be one or more solutions. 0 B. There will always be infinitely many solutions ° C. Usually there will be infinitely many solutions, but occasionally there will be no solutions 0 D. There will always be a solution. 0 E. Usually there will be infinitely many solutions, but occasionally there will be one or no solu- tions. 0 F. There will always be exactly one solution. O G. Usually there will be one solution, but occasionally there will be no solutions or infinitely O H. There will never be a solution. many solutions.

Explanation / Answer

A linear equation with 3 unknowns is a plane in 3D Geometry;  
2 such linear equations mean 2 planes; Now imagine two planes in a 3 D setup;

So usually, 2 planes in a 3-D space can coincide in a line (infinite solutions since there are infinite points on a line)
But, if e planes are parallel, there will be no solution (since there is no point of intersection of these 2 planes)

Hence, answer is option (C)

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