One of the most important and conceptual question from linear equations in two variables in which we have given two equations x+2y=5, 3x+ky+15=0 and we have to find the value of k for which it has a unique solution and also asked to solve for which it has no solution
Kindly solve the above equations
RS Aggarwal, Class 10, chapter 3D, question no 13
(i)
x+2y=5,3x+ky+15=0
Here,
a1=1, b1=2, c1=−5
a2=3, b2=k, c2=15
a1/a2=1/2, b1/b2=2/k, c1/c2=−5/15=−1/3
a unique solution
a1/a2≠b1/b2⇒1/2≠2/k
k≠4
(ii) a1/a2≠b1/b2≠c1/c2
1/2=2/k≠-1/3
k=4