Solve the following system of equations:2/x + 5/y = 1;60/x + 40/y = 19

1.	Solve the following system of equations:2/x + 5/y = 1;60/x + 40/y = 19
Answer» 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.

Answer»

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.

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