Question

For the pair of equation $\lambda x+3y+7=0$ and $2x+by-14=0$ to have infinitely many solutions, the value of ${}^{\prime }{\lambda }^{\prime }$ should be 1. Is the statement is true ? Give reasons.

Answer 1

Given : two lines $\Rightarrow \lambda x+3y+7=0,2x+by-14=0$

It two lines $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ are having infinitely many solutions,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\Rightarrow$ should be there

So, we can write -

$\frac{\lambda }{2}=\frac{3}{b}=\frac{7}{-14}\Rightarrow \frac{\lambda }{2}=\frac{7}{-14}\Rightarrow \frac{\lambda }{2}=\frac{1}{-2}$

So, $\lambda =-1$

So, the given statement is not true.