Q. 275.0( 2 Votes )

Show that each of

Answer :

Given: - Two equation x + 2y = 5 and 3x + 6y = 15


Tip: - We know that


For a system of 2 simultaneous linear equation with 2 unknowns


(iv) If D ≠ 0, then the given system of equations is consistent and has a unique solution given by



(v) If D = 0 and D1 = D2 = 0, then the system is consistent and has infinitely many solution.


(vi) If D = 0 and one of D1 and D2 is non – zero, then the system is inconsistent.


Now,


We have,


x + 2y = 5


3x + 6y = 15


Lets find D



D = – 6 – 6


D = 0


Again, D1 by replacing 1st column by B


Here




D1 = 30 – 30


D1 = 0


And, D2 by replacing 2nd column by B


Here




D2 = 15 – 15


D2 = 0


So, here we can see that


D = D1 = D2 = 0


Thus,


The system is consistent with infinitely many solutions.


Let


y = k


then,


x + 2y = 5


x = 5 – 2k


By changing value of k you may get infinite solutions


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Three schools A, Mathematics - Board Papers

Using properties Mathematics - Board Papers

Two schools A andMathematics - Board Papers

State True or FalMathematics - Exemplar