Solve for x and y:\(\frac{5}x-\frac{3}y=1\),\(\frac{3}{2x}+\frac{2}{3y

1.	Solve for x and y:\(\frac{5}x-\frac{3}y=1\),\(\frac{3}{2x}+\frac{2}{3y}=5\)
Answer» The given equations are: \(\frac{5}x-\frac{3}y=1\)..........(i) \(\frac{3}{2x}+\frac{2}{3y}=5\).......(ii) Putting 1/x = u and 1/y = v, we get: 5u - 3v = 1 …….(iii) ⇒ 3/2 u + 2/3 v = 5 ⇒ \(\frac{9u+4v}6\) = 5 ⇒ 9u + 4v = 30 …….(iv) On multiplying (iii) by 4 and (iv) by 3, we get: 20u - 12v = 4 ……..(v) 27u + 12v = 90 ……..(vi) On adding (iv) and (v), we get: 47u = 94 ⇒ u = 2 ⇒ 1/x = 2 ⇒ x = 1/2 On substituting x = 1/2 in (i), we get: \(\frac{\frac{5}1}2\) - \(\frac{3}y\) = 1 ⇒ 10 - 3/y = 1 ⇒ 3/y = (10 – 1) = 9 y = 3/9 = 1/3 Hence, the required solution is x = 1/2 and y = 1/3 .

Solve for x and y:\(\frac{5}x-\frac{3}y=1\),\(\frac{3}{2x}+\frac{2}{3y}=5\)

Answer»

The given equations are:

\(\frac{5}x-\frac{3}y=1\)..........(i)

\(\frac{3}{2x}+\frac{2}{3y}=5\).......(ii)

Putting 1/x = u and 1/y = v, we get:

5u - 3v = 1 …….(iii)

⇒ 3/2 u + 2/3 v = 5

⇒ \(\frac{9u+4v}6\) = 5

⇒ 9u + 4v = 30 …….(iv)

On multiplying (iii) by 4 and (iv) by 3, we get:

20u - 12v = 4 ……..(v)

27u + 12v = 90 ……..(vi)

On adding (iv) and (v), we get:

47u = 94 ⇒ u = 2

⇒ 1/x = 2 ⇒ x = 1/2

On substituting x = 1/2 in (i), we get:

\(\frac{\frac{5}1}2\) - \(\frac{3}y\) = 1

⇒ 10 - 3/y = 1 ⇒ 3/y = (10 – 1) = 9

y = 3/9 = 1/3

Hence, the required solution is x = 1/2 and y = 1/3 .