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
Solve the following system of equations graphically:
$x\ +\ y\ =\ 3$
$2x\ +\ 5y\ =\ 12$
Given:
The given system of equations is:
$x\ +\ y\ =\ 3$
$2x\ +\ 5y\ =\ 12$
To do:
We have to represent the above system of equations graphically.
Solution:
The given pair of equations are:
$x\ +\ y\ -\ 3\ =\ 0$....(i)
$y=3-x$
$2x\ +\ 5y\ -\ 12\ =\ 0$....(ii)
$5y=12-2x$
$y=\frac{12-2x}{5}$
To represent the above equations graphically we need at least two solutions for each of the equations.
For equation (i),
If $x=0$ then $y=3-0=3$
If $y=0$ then $0=3-x$
$x=3$
| $x$ | $0$ | $3$ |
$y=3-x$ | $3$ | $0$ |
For equation (ii),
If $x=0$ then $y=\frac{12-2(0)}{5}=\frac{12}{5}$ which is not an integer and so it is difficult to locate on the graph.
If $x=1$ then $y=\frac{12-2(1)}{5}=\frac{12-2}{5}=\frac{10}{5}=2$
If $x=-4$ then $y=\frac{12-2(-4)}{5}=\frac{12+8}{5}=\frac{20}{5}=4$
| $x$ | $1$ | $-4$ |
| $y=\frac{12-2x}{5}$ | $2$ | $4$ |
The above situation can be plotted graphically as below:
The line AB represents the equation $x+y-3=0$ and the line PQ represents the equation $2x+5y-12=0$.
The solution of the given system of equations is the intersecting point of both the lines.
Hence, the solution of the given system of equations is $x=1$ and $y=2$.
143 Views
