please give a brief explanation to why you chose the answer 15. If one is solvin

Question

please give a brief explanation to why you chose the answer

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

Explanation / Answer

Usually, when there are 3 quations , we can find the one solution.

Ex x+ y + z = 3

x + y - z =1

2x+ 3y + 4z = 9

Here only one solution exist i.e x=1,y=1,z=1

But some time there doesn't exist any solution.

x+ y + z = 2

2x + 2y + 2z = 4

-x - y - z =-6

There is no solution.

Also some times the no. of solution is infinite.

x+ y + z = 3

2x + 2y + 2z = 6

x+ y - z = 1

Here infinitely many solution exist as x=k,y= 2-k,z =1

So H is correct

H. Usually there will be one solution, but occassionally there will be no solution or infinetely many solutions.

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