Solve for x and y: 7(y + 3) – 2(x + 2) = 14, 4(y – 2) + 3(x – 3

1.	Solve for x and y: 7(y + 3) – 2(x + 2) = 14, 4(y – 2) + 3(x – 3) = 2
Answer» The given equations are: 7(y + 3) – 2(x + 2) = 14 ⇒ 7y + 21 – 2x – 4 = 14 ⇒ -2x + 7y = -3 ……..(i) and 4(y – 2) + 3(x – 3) = 2 ⇒ 4y – 8 + 3x – 9 = 2 ⇒ 3x + 4y = 19 ……….(ii) On multiplying (i) by 4 and (ii) by 7, we get: - 8x + 28y = -12 ……(iii) 21x + 28y = 133 ……(iv) On subtracting (iii) from (iv), we get: 29x = 145 ⇒ x = 5 On substituting x = 5 in (i), we get: -10 + 7y = -3 ⇒ 7y = (-3 + 10) = 7 ⇒ y = 1 Hence, the solution is x = 5 and y = 1.

Solve for x and y: 7(y + 3) – 2(x + 2) = 14, 4(y – 2) + 3(x – 3) = 2

Answer»

The given equations are:

7(y + 3) – 2(x + 2) = 14

⇒ 7y + 21 – 2x – 4 = 14

⇒ -2x + 7y = -3 ……..(i)

and 4(y – 2) + 3(x – 3) = 2

⇒ 4y – 8 + 3x – 9 = 2

⇒ 3x + 4y = 19 ……….(ii)

On multiplying (i) by 4 and (ii) by 7, we get:

- 8x + 28y = -12 ……(iii)

21x + 28y = 133 ……(iv)

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

29x = 145

⇒ x = 5

On substituting x = 5 in (i), we get:

-10 + 7y = -3

⇒ 7y = (-3 + 10) = 7

⇒ y = 1

Hence, the solution is x = 5 and y = 1.