In 'Completing The Analogous Pair', two words are given. These words are related to each other in some way. Another word is also given. The candidate is required to find out the relationship between the first two words and choose the word from the given alternatives, which bears the same relationship to the third word, as the first two bear.

The equations 4x + 7y - 10 =0 and 20x + 35y - 50 = 0 are :

###### Option:
A. consistent and have a unique solution.
B. consistent and have infinitely many solutions.
C. inconsistent.
D. None of these
Answer: B . consistent and have infinitely many solutions.

Justification:

Equation I:-  4x + 7y = 10
Equation II:- 20x + 35y = 50

.`. Multiply Equation I by 5.
(4x + 7y = 10) x (5) = (20x + 35y = 50)
We get Equation III = 20x + 35y = 50
Now, Subtract Equation III with Equation II.
(20x + 35y = 50) - (20x + 35y = 50)
.`. (20x - 20x) + (35y - 35y) = (50 - 50)
.`. (0) + (0) = (0)

So, the given equations, have an infinite number of solutions and hence they are consistant also.

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