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If the system of equations x + 2y + 3z = 3 4x + 3y - 4z = 4 8x + 4y - λz = 9 + μ has infinitely many solutions, then the ordered pair (λ, μ) is equal to :

1. (-72/5, 21/5)
2. (72/5, -21/5)
3. (72/5, 21/5)
4. (-72/5, -21/5)

Correct answer: (72/5, -21/5)

Solution

The correct option is derived from the condition that for the system to have infinitely many solutions, the third equation must be a linear combination of the first two equations. By substituting the values of λ and μ, we confirm that they satisfy this condition, ensuring consistency among the equations.

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