Solution for the given system of equation is
x+y−82 = x+2y−148 = 3x+y−1211
(2,6)
x+y−82 = x+2y−148⇒ 8(x + y - 8) = 2(x + 2y - 14) ⇒ 3x + 2y - 18 = 0 -----------(i)
x+2y−148 = 3x+y−1211⇒ 11(x +2 y - 14) = 8(3x + y - 12) ⇒ -13x + 14y - 58 = 0 -----------(ii)
Multiply (i) by 7, 21x + 14y - 126 = 0 -----------(iii)
then subtract from (iii) from (ii); we get
34x = 68 ⇒ x = 2
y = 6 [by substituting value of x=2 in (i)]