Question

In the system of equations, r and s are constants. If the system has infinitely many solutions, what is the value of rs?

Answer 1

Answer:  B) -48

Step-by-step explanation:

If the system of two linear equations $a_1x+b_1y=c_1\ \&\ a_2+b_2y=c_2$ has infinitely many solutions , then

$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}=k$

For the given system of linear equations : $rx-sy=26\\4x+3y=13$

We , will have

$\dfrac{r}{4}=\dfrac{-s}{3}=\dfrac{26}{13}=2\\\\\Rightarrow\ r= 4\times2=8\ \ \&\ \ s=2\times-3=-6$

The value of $rs=(8)\times-6=-48$

Hence, the value of rs is -48.

Thus , the correct option is B) -48.