In this question many people get trapped.
Method-1:
For given equations Augmented matrix[A|b] is :
R2→ R2+R1
R3→R3+R1
Then
R3→R3-2R2
After converting into echelon form we obtain:
After seeing [00…0] we think that infinite solution is the correct answer
But the catch here is for infinite solution there must me atleast one free column. But in this case there is no free column so the answer here is unique solution
Method-2:
The matrix is 3X2 matrix
Find rank[A] and rank[A|b]
rank[A] = 2
rank[A|b]=2
So number of free columns = 0
So there will be unique solution
therefore the option-C is correct