This is the basic and conceptual question from linear equations in two variables in which we have given two equations (a-1)x+3y=2, 6x+(1-2b)y=6 and we have been asked to find the value of a and b for which it has infinite solutions
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 3D, question no 21
The given system of equations can be written as
(a – 1) x + 3y = 2
⇒(a – 1) x + 3y – 2 = 0 ….(i) and
6x + (1 – 2b)y = 6
⇒6x + (1 – 2b)y – 6 = 0 ….(ii)
These equations are of the following form:
a1x+b1y+c1 = 0
a2x+b2y+c2 = 0
where, a1 = (a – 1), b1= 3, c1 = -2 and a2 = 6, b2 = (1 – 2b), c2 = -6
For an infinite number of solutions, we must have: