Question

For the system of linear equations 2x + 3y + 5z = 9, 7x + 3y - 2z = 8 and 2x + 3y +$\lambda$z $=\mu$.Under what condition does the above system of equations have infinitely many solutions.

• A. $\lambda =5$ and $\mu \ne 9$
• B. $\lambda =5$ and $\mu =9$
• C. $\lambda =9$ and $\mu \ne 5$
• D. $\lambda =9$ and $\mu =5$

Answer 1

The correct option is B $\lambda =5$ and $\mu =9$

$2x+3y+5z=9$,

$7x+3y-2z=8$,

$2x+3y+\lambda z=\mu$

Now, for infinitely many solutions. If $2$ equations out of $3$ are same then we are left with only $2$ equations with $3$ variables, this will give infinite solutions. Now if $\lambda =5$, $\mu =9$, then equation (i) and (iii) will be same and the system will have infinite solutions.

Hence, B is correct.