Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
For what value of $k$, the pair of linear equations $2kx+5y=7,6x-5y=11$ has a unique solution.
Given: The pair of linear equations $2kx+5y=7,\ 6x-5y=11$ has a unique solution.
To do: To find the value of $k$ for unique solution.
Solution:
The equation are:
$2kx+5y-7=0$
$6x-5y-11=0$
Here, $a_1=2k,\ b_1=5,\ c_1=-7$
And $a_2=6,\ b_2=-5,\ c_2=-11$
For the system to have unique solution
$\Rightarrow \frac{a_1}{a_2}\
eq\frac{b_1}{b_2}$
eq\frac{b_1}{b_2}$
$\Rightarrow \frac{2k}{6}\
eq\frac{5}{-5}$
eq\frac{5}{-5}$
$\Rightarrow 2k\
eq-\frac{6\times5}{5}$
eq-\frac{6\times5}{5}$
$\Rightarrow 2k\
eq-6$
eq-6$
$\Rightarrow k\
eq-\frac{6}{2}=-3$
eq-\frac{6}{2}=-3$
Thus, for $k\
eq-3$ the given system of equations have unique solution.
eq-3$ the given system of equations have unique solution.
Updated on: 10-Oct-2022
244 Views
Advertisements