Question

2/x+5/y=1/4

3/x+6/y=1/3

find x and y​

Answer 1

Equation 1: 2/x +5/y =1/4

2y+5x/xy =1/4

4(2y+5x)= xy

8y+20x = xy

Equation 2: 3/x+6/y =1/3

3y+6x/xy=1/3

9y+ 18x = xy

equation 1 and 2 is equal, because both the RHS is xy... We are equating these two equation

9y+18x=8y+20x

9y-8y= 20x-18x

y=2x (equation 3)

Now substitute equation 3 in equation 1's non simplified equation

2y+ 5x/xy =1/4

2(2x)+5x/ (2x) (x)= 1/4

4x+5x/2x^2=1/4

9x/2x^2 =1/4

9/2x=1/4 (cancelling x in numerator and x in denominator)

9*4=2x

36=2x

36/2= x

x=18

y=2x. (equation 3)

y=2(18)

y=36

Therefore,

x=18

y=36

Hoping that my answer could help u