If (x + y - 8)/2 = (x + 2y - 14)/3 = (3x + y - 12)/11 then find the values of x and y, respectively.

Given,
(x + y - 8)/2 = (x + 2y - 14)/3 = (3x + y - 12)/11
⇒ (x + y - 8)/2 = (x + 2y - 14)/3
⇒ 3x + 3y - 24 = 2x + 4y - 28
⇒ 3x + 3y - 2x - 4y = -28 + 24
x - y = -4 ...(i)
Again, (x + 2y - 14)/3 = (3x + y - 12)/11
⇒ 11x + 22y - 154 = 9x + 3y - 36
⇒ 2x + 19y = 118 ..(ii)
On multiplying Eq. (i) by 2 and subtracting from Eq., we get
2x - 2y = -8
2x + 19y = 118
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-21y = -126
∴ y = 6
On putting the value of y in Eq. (i), we get
x - 6 = -4
∴ x = 2
∴ x = 2 and y = 6