- 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:
$\frac{x}{7}\ +\ \frac{y}{3}\ =\ 5$
$\frac{x}{2}\ –\ \frac{y}{9}\ =\ 6$
Given:
The given system of equations is:
$\frac{x}{7}\ +\ \frac{y}{3}\ =\ 5$
$\frac{x}{2}\ –\ \frac{y}{9}\ =\ 6$
To do:
We have to solve the given system of equations.
Solution:
The given system of equations can be written as,
$\frac{x}{7}+\frac{y}{3}=5$
$\Rightarrow \frac{3(x)+7(y)}{21}=5$
$\Rightarrow 3x+7y=5(21)$ (On cross multiplication)
$\Rightarrow 3x+7y=105$---(i)
$\frac{x}{2}-\frac{y}{9}=6$
$\Rightarrow \frac{9(x)-2(y)}{18}=6$
$\Rightarrow 9x-2y=6(18)$ (On cross multiplication)
$\Rightarrow 9x=2y+108$
$\Rightarrow x=\frac{2y+108}{9}$----(ii)
Substitute $x=\frac{2y+108}{9}$ in equation (i), we get,
$3(\frac{2y+108}{9})+7y=105$
$\frac{2y+108}{3}+7y=105$ 
Multiplying by $3$ on both sides, we get,
$3(\frac{2y+108}{3})+3(7y)=3(105)$
$2y+108+21y=315$
$23y=315-108$
$23y=207$
$y=\frac{207}{23}$
$y=9$
Substituting the value of $y=9$ in equation (ii), we get,
$x=\frac{2(9)+108}{9}$
$x=\frac{18+108}{9}$
$x=\frac{126}{9}$
$x=14$
Therefore, the solution of the given system of equations is $x=14$ and $y=9$.