Question
Question: Let a and b be real numbers such that the equations 2x + 3y = 4 and ax – by = 7 have exactly one so...
Let a and b be real numbers such that the equations
2x + 3y = 4 and ax – by = 7 have exactly one solution, then which of the following system of equations also have exactly one solution ?
A
12x – 8y = 9, bx + ay = 0
B
12x – 8y = 9, ax + by = 0
C
12x – 8y = 0, ax + by = 9
D
None of these
Answer
12x – 8y = 9, bx + ay = 0
Explanation
Solution
If the given system has exactly one solution then
D ¹ 0 Ž – 2b – 3a ¹ 0 Ž 3a + 2b ¹ 0
Now 'D' of the system in (1)
= 12a + 8b = 4(3a + 2b) ¹ 0