Question

Solve the following systems of equations:
1/(7x) + 1/(6y) = 3
1/(2x) – 1/(3y) = 5

Answer 1

x = 1/14  ; y = 1/6

Step-by-step explanation:

Let 1/x = u and 1/y = v

 1/(7x) + 1/(6y) = 3

 1/7(u) +1/6(v) = 3

  6u  + 7v = 126 ------------(1)  

 1/(2x) – 1/(3y) = 5

 1/2 (u) - 1/3 (v) = 5

  3u - 2v = 30 ------------(2)

(2)*2, we get: 6u - 4v = 60 -----(3)

Subtracting 3 from 1, we get: 11v = 66

Therefore v = 6

Substituting in (2), we get: 3u -12 = 30

Therefore u = 14

So u = 1/x = 14. Therefore x = 1/14

So v = 1/y = 6. Therefore y =  1/6