Question

Solve the following systems of equation:

`3x - (y + 7)/11 + 2 = 10`

`2y + (x + 10)/7 = 10`

Answer 1

The given systems of equation is

`3x - (y + 7)/11 + 2 = 10`   ...(i)

`2y + (x + 11)/7 = 10`      ...(ii)

From (i), we get

`(33x - y - 7 + 22)/11 = 10`

⇒ 33x - y + 15 = 10 × 11

⇒ 33x + 15 - 110 = y

⇒ y = 33x - 95

From (ii) we get

`(14y + x + 11)/7 = 109`

⇒ 14y + x + 11 = 10 × 7

⇒ 14y + x + 11 = 70

⇒ 14y + x = 70 - 11

⇒ 14y + x = 59    ...(iii)

Substituting y = 33x - 95 in (iii), we get

14 (33x - 95) + x = 59

⇒ 462x - 1330 + x  = 59

⇒ 463x = 59 + 1330

⇒ 463x = 1389

⇒ x = `1389/463` 

⇒ x = 3

Putting x = 3, in y = 33x - 95, we get

y = 33 × 3 - 95

y = 99 - 95

y = 4

Hence, solution of the given system of equation is x = 3, y = 4.