Question

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

rx-sy=26

4x+3y=13


A) -14

B) -48

C) 14

D) 48

Answer 1

Answer: B) -48

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

`(a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2)=k`

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

We , will have

`(r)/(4)=(-s)/(3)=(26)/(13)=2\\\\\Rightarrow\ r= 4*2=8\ \ \&\ \ s=2*-3=-6`

The value of
`rs=(8)*-6=-48`

Hence, the value of rs is -48.

Thus , the correct option is B) -48.