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/c12=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