Question

Solve the following systems of equations:

`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 xx 11`

`=> 33x + 15 - 110 = y`

=> y = 33x - 95

From (ii) we get

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

`=> 14y + x + 11 = 10 xx 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 = 3`

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

`y = 33 xx 3 - 95`

`=> y = 99- 95`

= 4

y = 4

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