Question

Question 4
For the pair of equations $\lambda$x+3y+7=0 and 2x + 6y – 14 = 0. To have infinitely many solutions, the value of l should be 1. Is the statement true ? Give reasons

Answer 1

No, the given pair of linear equations
$\lambda$ x+3y+7=0 and 2x + 6y – 14 = 0
$Here,a_1=\lambda ,b_1=3,c_1=7,a_2=2,b_2=6,c_2=-14$
$If\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$ then system has infinitely many solutions
$\Rightarrow \frac{\lambda }{2}=\frac{3}{6}=-\frac{7}{14}\frac{\lambda }{2}=\frac{3}{6}=\lambda =1and\frac{\lambda }{2}=-\frac{7}{14}\Rightarrow \lambda =-1$
hence, $\lambda$ = -1 does not have a unique value
so, for no value of $\lambda$ the given pair of linear equations has infinitely many solutions