Question

If the system of linear equations
$x + y + z = 5$
$x + 2y + 2z = 6$
$x + 3y + \lambda = \mu , (\lambda, \mu \in R)$,has infinitely many solutions, then the value of $\lambda + \mu $ is:

• A. 12
• B. 10
• C. 9
• D. 7

Answer 1

Answer: (B)

$x + 3y + \lambda z - \mu = p (x + y + z -5) + q ( x + 2y + 2z - 6)$
on comparing the coefficient;
$p + q = 1 $ and $p + 2 q = 3$
$\Rightarrow \; ( p , q) = ( - 1 , 2 )$
Hence $x + 3y + \lambda z - \mu = x + 3y + 3z -7 $
$ \Rightarrow \; \lambda = 3 , \mu = 7 $