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Question
Solve for x and y:
`(x + y - 8)/2 = (x + 2y -14)/3 = (3x + y - 12)/11`
Solution
The given equations are:
`(x + y - 8)/2 = (x + 2y -14)/3 = (3x + y - 12)/11`
i.e.,`( x+y−)/2 = (3x+y−12)/11`
By cross multiplication, we get:
11x + 11y – 88 = 6x + 2y – 24
⇒11x – 6x + 11y – 2y = -24 + 88
⇒5x + 9y = 64 …….(i)
and `(x+2y−14)/3 = (3x+y−12)/11`
⇒11x + 22y – 154 = 9x + 3y – 36
⇒11x – 9x + 22y – 3y = -36 + 154
⇒2x + 19y = 118 …….(ii)
On multiplying (i) by 19 and (ii) by 9, we get:
95x + 171y = 1216 ……(iii)
18x + 171y = 1062 ……(iv)
On subtracting (iv) from (iii), we get:
77x = 154
⇒x = 2
On substituting x = 2 in (i), we get:
10 + 9y = 64
⇒9y = (64 – 10) = 54
⇒y = 6
Hence, the solution is x = 2 and y = 6.
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