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(a) Show that the equations x +y +z = 6 ...

(a) Show that the equations `x +y +z = 6 , x + 2y + 3z = 14 , x + 4y + 7z = 30` are consistent and solve them .

Answer

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Knowledge Check

  • The system of equations x +2y+3z=1, x-y+4z=0, 2x+y+7z=1 has

    A
    One solution
    B
    Two solution
    C
    No solution
    D
    Infinitely many solution
  • The distance between the planes x + 2y + 3z + 7 = 0 and 2x + 4y + 6z + 7 = 0 is

    A
    `(sqrt(7))/(2sqrt(2))`
    B
    `(7)/(2sqrt(14))`
    C
    `(sqrt(7))/(2)`
    D
    `(7)/(2sqrt(2))`
  • The distance between the planes x + 2y + 3z + 7 = 0 and 2x + 4y + 6z + 7 0 is

    A
    `(sqrt7)/(2sqrt2)`
    B
    `(7)/(2)`
    C
    `(sqrt7)/(2)`
    D
    `(7)/(2sqrt(2))`
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