# If the system of linear equations x + y + z = 5x + 2y + 2z = 6x + 3y + z = , ( ,  ) , has infinitelymany solutions, then the value of + is : Option 1) 12 Option 2) 9 Option 3) 7 Option 4) 10

x + 3y + z - = p ( x + y + z - 5) + q ( x + 2y + 2z - 6 )

On comparing the coefficients

p + q = 1   and    p + 2q = 3

=> ( p , q ) = ( -1 , 2 )

Hence, x + 3y + z - = x + 3y + 3z - 7

=> => So, option (4) is correct.

Option 1)

12

Option 2)

9

Option 3)

7

Option 4)

10

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