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)

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