- 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
By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve them.
$ x+y=3 $
$ 3 x+3 y=9 $
Given:
Pair of linear equations:
\( x+y=3 \)
\( 3 x+3 y=9 \)
To do:
We have to find whether the given pair of linear equations is consistent /inconsistent. If consistent, then obtain the solution graphically.
Solution:
$x+y-3=0$.........(i)
$3x+3y-9=0$.........(ii)
Here,
$a_{1}=1, b_{1}=1, c_{1}=-3$
$a_{2}=3, b_{2}=3, c_{2}=-9$
$\frac{a_{1}}{a_{2}}=\frac{1}{3}$
$\frac{b_{1}}{b_{2}}=\frac{1}{3}$
$\frac{c_{1}}{c_{2}}=\frac{-3}{-9}$
$=\frac{1}{3}$
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}}=\frac{c_1}{c_2}$
This implies,
The given pair of lines is coincident and therefore consistent.
For equation (i),
$y=3-x$
$x$ | 0 | $3$ |
$y$ | $3$ | $0$ |
Plot point $( 0,\ 3)$ and $(3,\ 0)$ on a graph and join then to get equation $x+y=3$
For equation (ii),
$3y=9-3x$
$y=3-x$
$x$ | $0$ | 3 |
$y$ | $3$ | 0 |
Plot points $(0,\ 3)$ and $(3,\ 0)$ on a graph and join them to get equation $3x+3y=9$
There are infinite solutions as the lines are coincident.