Question

Solve for x and y: 

`2x + 5y = 8/3, 3x - 2y = 5/6`

Answer 1

The given equations are: 

`2x + 5y = 8/3`   ...(i)

`3x - 2y = 5/6`   ...(ii)

On multiplying (i) by 2 and (ii) by 5, we get:

`4x + 10y = 16/3`   ...(iii)

`15x - 10y = 25/6`   ...(iv)

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

`19x = 57/6`

⇒ `x =  57/(6 xx 19)`

⇒ `x =  57/114`

⇒ `x = 3/6`

⇒ `x = 1/2`

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

`2 × 1/2 + 5y = 8/3`

⇒ `5y = (8/3 - 1)`

⇒ `5y = 5/3`

⇒ `y = 5/(3 × 5)`

⇒ `y = 5/15`

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