One of the most important and conceptual question from linear equations in two variables in which we have been asked to find the value of variables x and y from the equations x+6/y=6, 3x-8/y=5

Kindly solve these equations

RS Aggarwal, Class 10, chapter 3B, question no 19

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.