An important and conceptual question from linear equations in two variables in which we have given two equations kx+2y=5, 3x-4y=10 and we have been asked to find the value of k in such a way that it has a unique solution and also asked to solve these equations in such a way that it has no solution
RS Aggarwal, Class 10, chapter 3D, question no 12
(i) Here,
a1​=k, b1​=2, c1​=5
a2​=3, b2​=−4, c2​=10
a1/a2​​=k/3, b1/b2​​=2/-4​=−1/2​
c1/c1​​2=5​/10=1/2​
System has a unique solution.
a1/a2≠b1/b2​​⇒k/3≠-1/2​
k≠−3/2
(ii) If system has a no solution.
a1/a2=b1/b2​​≠1/2​
k/3=−1​/2≠1/2​
k≠3/2