![Trending Articles on Technical and Non Technical topics](/images/trending_categories.jpeg)
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 a and b, the following system of equations have an infinite number of solutions.$2x+3y=7; (a-b)x+(a+b)y=3a+b-2$
Given: System of the equations $2x+3y=7;\ (a-b)x+(a+b)y=3a+b-2$
To do: To find the value of $a$ and $b$.
Solution:
$2x+3y=7$
$(a−b)x+(a+b)y=3a+b−2$
$\because$ It has infinitely many solutions.
$\therefore \frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
$\frac{2}{a−b}=\frac{3}{a+b}=\frac{7}{3a+b−2}$
From $( i)$ and $( ii)$
$\frac{3}{a+b}=\frac{7}{3a+b−2}$
$7a+7b=9a+3b−6$
$\Rightarrow 2a−4b=6$
$\Rightarrow a−2b=3$
$\Rightarrow 5b−2b=3$
$\Rightarrow 3b=3\Rightarrow b=1$
$\therefore a=5\times 1=5$.
Advertisements