Question

What should be the value of $\lambda$ for the given equations to have infinity many solutions? $5x+\lambda$ $y=4$ and $15x+3y=12$

Answer 1

Given equations will have infinity solutions, if and only if they satisfy the condition,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

$5x+\lambda y=4\to a_1=5,b_1=\lambda ,c_1=5$

$15x+3y=12\to a_2=15,b_2=3,c_2=12$

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}=\frac{5}{15}=\frac{\lambda }{3}=\frac{4}{12}$

$=\frac{1}{3}=\frac{\lambda }{3}=\frac{1}{3}$

$\therefore \lambda$ should be equal to $1$

$\lambda =1$.