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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