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.