Question

The value of c for which the pair of equations $cx+y=2$ and $6x+2y=3$ will have infinitely many solutions is

• A. $-3$
• B. $3$
• C. $12$
• D. None of these

Answer 1

Answer: (D)

None of these

When there are two consistent equations as

$a_{1}x+b_{1}y+c_1=0\&a_{2}x+b_{2}y+c_2=0$ then the equations will have infintely many solutions when the lines are coincident

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

The equations are not coincident if $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

Here the equations are

$cx+y=2$ and $6x+2y=3$

So, $a_1=c,b_1=1,c_1=-2$ and $a_2=6,b_2=2,c_2=-3$

$\therefore \frac{a_1}{a_2}=\frac{c}{6},\frac{b_1}{b_2}=\frac{1}{2}$ and $\frac{c_1}{c_2}=\frac{-2}{-3}=\frac{2}{3}$

Here we see that, $\frac{b_1}{b_2}\ne \frac{c_1}{c_2}.$

The lines are not coincident.

i.e we cannot assign any value to c.