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Q.

If the system of equations
x + 2y – 3z = 2
2x + $λ$ y + 5z = 5
14x + 3y + $μ$ z = 33
has infinitely many solutions, then $λ$ + $μ$ is equal to:

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a

11

b

13

c

12

d

10

answer is D.

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Detailed Solution

$\begin{array}{l} D = |\begin{array}{ccc} 1 & 2 & - 3 \\ 2 & λ & 5 \\ 14 & 3 & μ \end{array}| = 0, λμ + 42 λ - 4 μ + 107 = 0 \\ D_{1} = 2 λμ + 99 λ - 10 μ + 255 \\ D_{2} = 13 - μ \\ D_{3} = 5 λ + 5 \\ D_{2} = 0 \Rightarrow μ = 13 & D_{3} = 0 \Rightarrow λ = - 1 \end{array}$

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