One of the most important and exam oriented question from linear equations in two variables in which we have given two equations kx-y=2, 6x-2y=3 and we have to find the value of k for which the given equations have a unique solution.
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, Chapter 3F, question no 17
The given system of equations is
kx−y−2=0
6x−2y−3=0
It is of the form a1x+b1y+c1=0
a2x+b2y+c2=0,
where a1=k, b1=−1, c1=−2 and a2=6, b2=−2 and c2=−3
(i) The given system will have a unique solution, if
a1/a2≠b1/b2 i.e, if k/6≠−1/-2 i.e., k≠3
So, the given of equations system will have a unique solution, if k≠3.