# How to solve 2/3x+2y+3/3x-2y=17/5 5/3x+2y+1/3x-2y=2 ?

Welcome to my article 2/3x+2y+3/3x-2y=17/5 5/3x+2y+1/3x-2y=2 ? This question is taken from the linear equation.
The solution of this question has been explained in a very simple way by a well-known teacher by doing addition, subtraction, and fractions.
For complete information on how to solve this question 2/3x+2y+3/3x-2y=17/5 5/3x+2y+1/3x-2y=2 ?, read and understand it carefully till the end.

Let us know how to solve this question 2/3x+2y+3/3x-2y=17/5 5/3x+2y+1/3x-2y=2 ?

First write the question on the page of the notebook

## 2/3x+2y+3/3x-2y=17/5 5/3x+2y+1/3x-2y=2 ?

on writing like this,

\displaystyle \frac{2}{{3x+2y}}+\frac{3}{{3x-2y}}=17 _ equation (1)

\displaystyle \frac{5}{{3x+2y}}+\frac{1}{{3x-2y}}=2 _equation (2)

suppose,
1 / (3x +2y) = m
And
1 / ( 3x-2y) = n

Then,

2m + 3n = 17/5 _ equation (3)

5m + n = 2 _ equation (4)

Multiplying by 5 in equation (3) and multiplying by 2 in equation (4) ,

\displaystyle \text{ }\left( {2m\text{ }+\text{ }3n\text{ }=\text{ }17/5} \right)\times 5 ,

\displaystyle \text{ }\left( {5m\text{ }-\text{ }n\text{ }=\text{ }2\text{ }} \right)\times 2 ,

10 m +15 n =17 _equation (5)

10 m + 2 n = 4 _equation (6)

Subtracting Equation (6) from Equation (5)

10 m – 10 m + 15 n – 2 n = 17 -4

13 n = 13

n = 13 / 13

## n = 1

Substituting the value of n in Equation (4),

5 m + n = 2

5 m +1 = 2

5 m = 2 – 1

5 m = 1

## m = 1 / 5

Substituting the value of m in the given 1/(3x +2y ) =m ,

\displaystyle \frac{1}{{3x+2y}}=m ,

\displaystyle \frac{1}{{3x+2y}}=\frac{1}{5} ,

on slant multiplication,

\displaystyle 3x+2y=5 , _equation (7)

Substituting the value of n in the given 1/(3x -2y ) =n ,

\displaystyle \frac{1}{{3x-2y}}=n ,

\displaystyle \frac{1}{{3x-2y}}=1 ,

\displaystyle 3x-2y=1 , _equation (8)

On adding equation (8) to equation (7),

3 x + 3 x + 2 y – 2 y = 5 + 1

6 x = 6

x = 6 / 6

## x = 1

Now putting x=1 in equation (7),

3 x + 2 y = 5

\displaystyle 3\times 1+2y=5 ,

\displaystyle 3+2y=5 ,

\displaystyle 2y=5-3 ,

\displaystyle 2y=2 ,

\displaystyle y=\frac{2}{2} ,

## y = 1

The intended solution to this question,

## x = 1 and y = 1 (answer)

This article 2/3x+2y+3/3x-2y=17/5 5/3x+2y+1/3x-2y=2 ? has been completely solved by tireless effort from our side, still if any error remains in it then definitely write us your opinion in the comment box. If you like or understand the methods of solving all the questions in this article, then send it to your friends who are in need.