One of the most important and conceptual question from linear equations in two variables in which we have given two equations (k-1)x-y=5, (k+1)x+(1-k)y=(3k+1) and we have to find the value of k for which the following equations has infinite solutions
Kindly solve the above equations
RS Aggarwal, Class 10, chapter 3D, question no 19
The given system of equations:
(k – 1)x – y = 5
⇒ (k – 1)x – y – 5 = 0 ….(i) And,
(k + 1)x + (1 – k)y = (3k + 1)
⇒ (k + 1)x + (1 – k)y – (3k + 1) = 0 …(ii)
These equations are of the following form: a1x+b1y+c1 = 0, a2x+b2y+c2 = 0 where, a1 = (k – 1), b1= -1, c1 = -5 and a2 = (k + 1), b2 = (1 – k), c2 = -(3k + 1)
For an infinite number of solutions, we must have: