Question

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, f are non-zero.
\[ ax + by = c \] \[ dx + ey = f \] A. \( a = kd \) and \( b = ke \), \( c = kf \), \( k \neq 0 \)
B. \( a = b = 1 \), \( d = e = 2 \), \( f = 2c \)

• A. The question can be answered by one of the statements alone but not by the other.
• B. The question can be answered by using either statement alone.
• C. The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
• D. The question cannot be answered even by using both statements together.

Hint:

When solving systems of equations, ensure that all parameters are provided, and check if each equation can be solved independently.

Answer 1

The Correct Option is B

From Statement A: We can solve the system of equations using this relationship for \( a, b, c, d, e, f \) and find a solution for \( x \) and \( y \).
From Statement B: Directly substituting these values into the equations allows us to find a specific solution for \( x \) and \( y \).
Since both statements give us enough information to solve for \( x \) and \( y \), the Correct Answer is (2).