This is the basic and conceptual question from linear equations in two variables in which we have given two equations 4x-5y=k, 2x-3y=12 and we have to find the value of k and also asked to solve the equations in such a way that it has a unique solution

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 3D, question no 8

Given system of equations is

4x−5y=k...(1)

2x−3y=12...(2)

Here

a1=4, b1=−5, c1=−k

a2=2, b2=−3, c2=−12

Condition for the system to have unique solution is

a1/a2≠b1/b2

Here, a1/a2=4/2=2 and b1/b2=5/3

Clearly 2≠5/7

Therefore, the given system will always have unique solution.

Therefore, k is any real number.