Solve for x and y:\(\frac{x}3+\frac{y}4= 11 \),\(\frac{5x}6-\frac{y}

1.	Solve for x and y:\(\frac{x}3+\frac{y}4= 11 \),\(\frac{5x}6-\frac{y}3+7= 0 \)
Answer» The given equations are: \(\frac{x}3+\frac{y}4= 11 \) ⇒ 4x + 3y = 132 …….(i) and \(\frac{5x}6-\frac{y}3+7= 0 \) ⇒ 5x – 2y = -42 ……..(ii) On multiplying (i) by 2 and (ii) by 3, we get: 8x + 6y = 264 …...(iii) 15x – 6y = -126 ….(iv) On adding (iii) and (iv), we get: 23x = 138 ⇒ x = 6 On substituting x = 6 in (i), we get: 24 + 3y = 132 ⇒ 3y = (132 – 24) = 108 ⇒ y = 36 Hence, the solution is x = 6 and y = 36.

Solve for x and y:\(\frac{x}3+\frac{y}4= 11 \),\(\frac{5x}6-\frac{y}3+7= 0 \)

Answer»

The given equations are:

\(\frac{x}3+\frac{y}4= 11 \)

⇒ 4x + 3y = 132 …….(i)

and \(\frac{5x}6-\frac{y}3+7= 0 \)

⇒ 5x – 2y = -42 ……..(ii)

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

8x + 6y = 264 …...(iii)

15x – 6y = -126 ….(iv)

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

23x = 138

⇒ x = 6

On substituting x = 6 in (i), we get:

24 + 3y = 132

⇒ 3y = (132 – 24) = 108

⇒ y = 36

Hence, the solution is x = 6 and y = 36.