\[x+y+z=5\] |
\[x+2y+2z=6\] |
\[x+3y+\lambda z=\mu ,\]\[(\lambda ,\mu \in R),\]has infinitely many solutions, then the value of \[\lambda +\mu \] is : |
A) 12
B) 10
C) 9
D) 7
Correct Answer: B
Solution :
\[x+3y+\lambda z-\mu =p(x+y+z-5)+\] \[q(x+2y+2z-6)\] on comparing the coefficient; \[p+q=1\]and \[p+2q=3\] \[\Rightarrow (p,q)=(-1,2)\] Hence \[x+3y+\lambda z-\mu =x+3y+3z-7\] \[\Rightarrow \lambda =3,\mu =7\]You need to login to perform this action.
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