Question

Solve the following pair of linear equation and verify the solution 2/x + 3/y = 13 and 5/x - 4/y = -2

Answer 1

Answer:

Equation - 1

2/x + 3/y = 13

Equation - 2

5/x - 4/y = (-2)

Subtracting Equation - 1 from 2

2/x +3/y - (5/x -4/y) = 13 - (-2)

or

2/x +3/y - 5/x + 4/y = 13 + 2

or

-3/x + 7/y = 15

or

-3y +7x /xy = 15

or

7x - 3y =15xy

or

7x = 15xy +3y

or

7x = 3y (5x + 1)

or

3y = 7x/5x+1

or

y = 7x/15x+3

Substituting the value of y in Equation - 1

2/x + 3/7x/15x+3 = 13

or

2/x + 3(15x+3)/7x = 13

or

2/x + 45x^2 + 9x/7x = 13

or

45x^2 +9x +14/7x = 13

or

45x^2 + 9x +14 = 91x

or

5x + 1 + 14 = 82/9

or

x+5 = 82/9/5

or

x= 82/45 - 9/45

or

x = 73/45