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Question:

Directions: Each question is followed by two statements I and II. Mark:
1. if the question can be answered by any one of the statements alone, but cannot be answered by using the other statement alone.
2. if the question can be answered by using either statement alone.
3. if the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
4. if the question cannot be answered even by using both the statements together.

Find a pair of real numbers x and y that satisfy the following two equations simultaneously. It is known that the values of a, b, c, d, e and f are non-zero.
ax + by = c
dx + ey = f
I. a = kd and b = ke, c = kf, k ≠ 0
II. a = b = 1, d = e = 2, f ≠ 2c

Explanation:

Statement I when used to solve the sum gives us the same equation as the second substituted in to the first equation.

kdx + key = kf
∴ k(dx + ey) = kf
as k ≠ 0, dx + ey = f which is same as second equation.
So it is of no use as we get infinite solutions and not a unique one.
Statement II gives us the following equations.
x + y = c
2x + 2y = f.
These are two linear equations in x and y, such that

$\frac{1}{2} = \frac{1}{2} \neq \frac{c}{f}$

As $\frac{c}{f} \neq \frac{1}{2}$ (Given), the system will have no solution.
As the data given in both the statements is inconsistent, the question cannot be answered.

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