Question

Solve the following system of equations:

2/x + 5/y = 1;

60/x + 40/y = 19

Answer 1

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

So, the given equations becomes

2u + 5v = 1…………(i)

60u + 40v = 19 …………(ii)

Multiplying equation (i) x 8 and (ii) x 1 we get,

16u + 40v = 8 …………(iii)

60u + 40v = 19 ………(iv)

Subtracting equation (iii) from (iv) we get,

60u – 16u + 40v – 40v = 19 – 8

⇒ 44u = 11

⇒ u = 1/4

Now putting u = 1/4 in equation (iv) we get,

60(1/4) + 40v = 19

⇒ 15 + 40v = 19

⇒ v = 4/ 40 = 1/10

Hence, x = 1/u = 4 and, y = 1/v = 10.