North west corner method, Mathematics

What is the history of North west corner method in transportation problem?

Why there are only m+n-1 solution to the transportation problem?

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( a+2b)x + (2a - b)y = 2, (a - 2b)x + (2a +b)y = 3 (Ans: 5b - 2a/10ab , a + 10b/10ab ) Ans: 2ax + 4ay = y , we get 4bx - 2by = -1 2ax+ 4ay = 5  4bx- 2by = - 1

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