If the system of equations
, ,
has infinitely many solutions, then equals
, ,
has infinitely many solutions, then equals
- A.8
- B.18
- C.21
- D.5
Show answer and solution
Correct option: A
Solution
From the first two equations, subtracting: y + 2z = 4. For infinitely many solutions, the third equation must be a linear combination of the first two. Subtracting the first from the third: 2y + (α-1)z = β-5. This must be consistent with y + 2z = 4, so 2y + 4z = 8, giving α-1 = 4 → α = 5 and β-5 = 8 → β = 13. Therefore β - α = 13 - 5 = 8.
[JEE Main 2019 · 10 Jan · Shift I]