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If the system of equations

x + y + z = 6

2x + 5y + aZ = b

x + 2y + 3z = 14

has infinitely many solutions, then α + β is equal to

Option 1 -

8

Option 2 -

36

Option 3 -

44

Option 4 -

48

0 4 Views | Posted 2 months ago
Asked by Shiksha User

  • 1 Answer

  • P

    Answered by

    Payal Gupta | Contributor-Level 10

    2 months ago
    Correct Option - 3


    Detailed Solution:

    Δ=0

    |1125α123|=0

    15 -2α +α- 6 – 1 = 0

    α = 8

    For = 8, equations are

    x + y + 3 = 6

    2x + 5y + 8z =β

    x + 2y + 3z = 14

    (2, 5, 8)=l (1, 1, 1)+m (1, 2, 3)

    2=l+m5=l+2m]→3=m, l=−1

    8 = l+3m

    β=6l+14m

    =- 6 + 42 = 36

    α + β = 8 + 36 = 44

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