Solve for x and y: 2x + 5y = 8/3 , 3x – 2y = 5/6

1.	Solve for x and y: 2x + 5y = 8/3 , 3x – 2y = 5/6
Answer» 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 × 19) = 3/6 = 1/2 On substituting x = 1/2 in (i), we get: 2 × 1/2 + 5y = 8/3 ⇒ 5y = ( 8/3 − 1) = 5/3 ⇒y = 5/ (3 × 5) = 1/3 Hence, the solution is x = 1/2 and y = 1/3 .

Answer»

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 × 19) = 3/6 = 1/2

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

2 × 1/2 + 5y = 8/3

⇒ 5y = ( 8/3 − 1) = 5/3

⇒y = 5/ (3 × 5) = 1/3

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

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