Question

The equations $\lambda x-y=2,2x-3y=-\lambda$ and $3x-2y=-\lambda$ are consistent for

• A. $\lambda =-4$
• B. $\lambda =1,4$
• C. $\lambda =1,-4$
• D. $\lambda =-1,4$
• E. $\lambda =-1$

Answer 1

Answer: (D)

In a consistent, the intersection point of two lines, satisfy the third line.
Consider $\lambda =-1$, then given equation become
$-x-y=2$
$2x-3y=1$
$\Rightarrow x=-1,y=-1$
Third equation is $3x-2y=-1$
Put $x=-1,y=-1$
$\therefore -3+2=-1$
$\Rightarrow -1=-1$, true
Consider $\lambda =4$, then given equation become
$4x-y=2$
$2x-3y=-4$
$\Rightarrow y=2,x=1$
Third equation is $3x-2y=-1$
Put $y=2,x=1$
$\therefore 3-4=-1$
$\Rightarrow -1=-1$, true