Q. 145.0( 6 Votes )

For what value of k does the system of equations

x + 2y = 3, 5x + ky + 7 = 0

have (i) a unique solution, (ii) no solution?

Also, show that there is no value of k for which the given system of equations has infinitely many solutions.

Answer :

(i) Given: x + 2y = 3 – eq 1


5x + ky + 7 = 0 – eq 2


Here,


a1 = 1, b1 = 2, c1 = - 3


a2 = 5, b2 = k, c2 = 7


Given systems of equations has a unique solution




k ≠10


k ≠ 10


(ii) Given: x + 2y = 3 – eq 1


5x + ky + 7 = 0 – eq 2


Here,


a1 = 1, b1 = 2, c1 = - 3


a2 = 5, b2 = k, c2 = 7


Given that system of equations has no solution


=


Here,


=


Here,


k = 10


k = 10


For the system of equations to have infinitely many solutions


= =


= = which is wrong.


That is, for any value of k the give system of equations cannot have infinitely many solutions.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Dealing With the Real Life ProblemsDealing With the Real Life ProblemsDealing With the Real Life Problems53 mins
Quiz | Solution of Linear EquationsQuiz | Solution of Linear EquationsQuiz | Solution of Linear Equations53 mins
Champ Quiz | Consistency and Inconsistency of SolutionsChamp Quiz | Consistency and Inconsistency of SolutionsChamp Quiz | Consistency and Inconsistency of Solutions36 mins
Pair of Linear Equations in Two VariablesPair of Linear Equations in Two VariablesPair of Linear Equations in Two Variables46 mins
Quiz | Real Life Problems Through Linear EquationsQuiz | Real Life Problems Through Linear EquationsQuiz | Real Life Problems Through Linear Equations56 mins
Smart Revision | Important Word ProblemsSmart Revision | Important Word ProblemsSmart Revision | Important Word Problems37 mins
Dealing with the Real Life ProblemsDealing with the Real Life ProblemsDealing with the Real Life Problems54 mins
Elimination (quicker than quickest)Elimination (quicker than quickest)Elimination (quicker than quickest)44 mins
Bonus on Applications of Linear Equations in Two VariablesBonus on Applications of Linear Equations in Two VariablesBonus on Applications of Linear Equations in Two Variables43 mins
HOT Topics of Applications of Linear Equations in Two VariablesHOT Topics of Applications of Linear Equations in Two VariablesHOT Topics of Applications of Linear Equations in Two Variables52 mins
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 :