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 which values of '$a$' and ' $b$ ' does the following pair of linear equations an infinite number of solutions $2x+3y=7,(a-b)x+(a+b)y=3a+b-2$.
Given: The following pair of linear equations an infinite number of solutions $2x+3y=7,(a-b)x+(a+b)y=3a+b-2$.
To do: To find the value of $a$ and $b$.
Solution:
Given equations are: $2x+3y=7$ ..... $( i)$
$( a-b)x+( a+b)y=3a+b-2$ ...... $( ii)$
As gievn, It has infinitely many solutions
Therefore, $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
$\Rightarrow \frac{2}{a-b}=\frac{3}{a+b}=\frac{7}{3a+b-2}$
$\frac{2}{a-b}=\frac{3}{a+b}$
$\Rightarrow 2( a+b)=3( a-b)$
$\Rightarrow 2a+2b=3a-3b$
$\Rightarrow a-5b=0$
$\Rightarrow a=5b$ ..... $( iii)$
Now, $\frac{3}{a+b}=\frac{7}{3a+b-2}$
$\Rightarrow 7a+7b=9a+3b-6$
$\Rightarrow 2a-4b=6$
$\Rightarrow a-2b=3$
$\Rightarrow 5b-2b=3$
$\Rightarrow 3b=3$
$\Rightarrow b=1$
$\therefore a=5\times1=5$ [$\because a=5b$ from $( iii)$]
Thus, $a=5$ and $b=1$.
Updated on: 10-Oct-2022
30 Views
Advertisements