Solve for x and y: 2x - 3y/ 4 = 3, 5x = 2y + 7

1.	Solve for x and y: 2x - 3y/ 4 = 3, 5x = 2y + 7
Answer» The given equations are: 2x - 3y/ 4 = 3 …..(i) 5x = 2y + 7 ……..(ii) On multiplying (i) by 2 and (ii) by 3/4 , we get: 4x - 3/2 y = 6 …...(iii) 15/4 x = 3/2 y + 21/ 4 ….(iv) On subtracting (iii) and (iv), we get: - 1/4 x = - 3/ 4 ⇒x = 3 On substituting x = 3 in (i), we get: 2 × 3 - 3y/4 = 3 ⇒ 3y/4 = (6 – 3) = 3 ⇒y = (3 ×4 )/3 = 4 Hence, the solution is x = 3 and y = 4.

Answer»

The given equations are:

2x - 3y/ 4 = 3 …..(i)

5x = 2y + 7 ……..(ii)

On multiplying (i) by 2 and (ii) by 3/4 , we get:

4x - 3/2 y = 6 …...(iii)

15/4 x = 3/2 y + 21/ 4 ….(iv)

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

- 1/4 x = - 3/ 4

⇒x = 3

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

2 × 3 - 3y/4 = 3

⇒ 3y/4 = (6 – 3) = 3

⇒y = (3 ×4 )/3 = 4

Hence, the solution is x = 3 and y = 4.

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