Solve for x and y: x + 6/y = 6, 3x - 8/y = 5

1.	Solve for x and y: x + 6/y = 6, 3x - 8/y = 5
Answer» The given equations are: x + 6/y = 6 ……..(i) 3x - 8/y = 5 ……..(ii) Putting 1/y = v, we get: x + 6v = 6 …….(iii) 3x – 8v = 5 ……(iv) On multiplying (iii) by 4 and (iv) by 3, we get: 4x + 24v = 24 ……..(v) 9x – 24v = 15 ……..(vi) On adding (v) from (vi), we get: 13x = 39 ⇒ x = 3 On substituting x = 3 in (i), we get: 3 + 6/y = 6 ⇒ 6/y = (6 – 3) = 3 ⇒ 3y = 6 ⇒ y = 2 Hence, the required solution is x = 3 and y = 2.

Answer»

The given equations are: x + 6/y = 6 ……..(i)

3x - 8/y = 5 ……..(ii)

Putting 1/y = v, we get:

x + 6v = 6 …….(iii)

3x – 8v = 5 ……(iv)

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

4x + 24v = 24 ……..(v)

9x – 24v = 15 ……..(vi)

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

13x = 39

⇒ x = 3

On substituting x = 3 in (i), we get:

3 + 6/y = 6

⇒ 6/y = (6 – 3) = 3

⇒ 3y = 6

⇒ y = 2

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

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