Question

Find the value of $k$ for which the given simultaneous equations have infinitely many solutions:

$4x+y=7;16x+ky=28$

• A. $k=2$
• B. $k=6$
• C. $k=3$
• D. $k=4$

Answer 1

The correct option is D $k=4$

As we know the condition for the pair of equations $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ to have infinite solutions is

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

$\therefore$ For infinite number of solutions,

$\frac{4}{16}=\frac{1}{k}=\frac{-7}{-28};\therefore k=4$