Solve for x and y:5/x + 6y = 13, 3/x + 4y = 7

1.	Solve for x and y:5/x + 6y = 13, 3/x + 4y = 7
Answer» The given equations are: 5/x + 6y = 13 ……..(i) 3/x + 4y = 7 ……..(ii) Putting 1/x = u, we get: 5u + 6y = 13 …….(iii) 3u + 4y = 7 ……(iv) On multiplying (iii) by 4 and (iv) by 6, we get: 20u + 24y = 52 ……..(v) 18u + 24y = 42 ……..(vi) On subtracting (vi) from (v), we get: 2u = 10 ⇒ u = 5 ⇒ 1/x = 5 ⇒ x = 1/5 On substituting x = 1/5 in (i), we get: 5/ 1/3 ⁄ + 6y = 13 25 + 6y = 13 6y = (13 – 25) = -12 y = -2 Hence, the required solution is x = 1/5 and y = -2

Answer»

The given equations are:

5/x + 6y = 13 ……..(i)

3/x + 4y = 7 ……..(ii)

Putting 1/x = u, we get:

5u + 6y = 13 …….(iii)

3u + 4y = 7 ……(iv)

On multiplying (iii) by 4 and (iv) by 6, we get:

20u + 24y = 52 ……..(v)

18u + 24y = 42 ……..(vi)

On subtracting (vi) from (v), we get:

2u = 10 ⇒ u = 5

⇒ 1/x = 5

⇒ x = 1/5

On substituting x = 1/5 in (i), we get:

5/ 1/3 ⁄ + 6y = 13

25 + 6y = 13

6y = (13 – 25) = -12

y = -2

Hence, the required solution is x = 1/5 and y = -2

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