Question

What value of b will cause the system to have an infinite number of solutions? y = 6x – b –3x + y = –3 b =

(a)2
(b) 4
(c) 6
(d) 8

Answer 1

Answer with explanation:

Consider two linear equation in two variable,

ax + by =c

p x +q y=r

The equations have an infinite number of solutions , means the two lines are Coincident, when it follows the following law

`(a)/(p)= (b)/(q)= (c)/(r)`

--------------------------------------(1)

Now, equation of two lines are

1. y= 6 x -b

→6 x -y -b=0

2. -3 x +y= -3

⇒-3 x+y+3=0

By the above law,that is law 1, the two lines will be coincident

`(6)/(-3)=(-1)/(1)= (-b)/(3)\\\\2=1= (b)/(3)`

Which is not possible that is ,2≠1.

→→→Hence the two lines can never be coincident for any value of b.