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Question
`(3)/x - (2)/y` = 0 and `(2)/x + (5)/y` = 19, Hence, find a if y = ax + 3.
Solution
`(3)/x - (2)/y` = 0 __________(1)
`(2)/x + (5)/y` = 19 _________(2)
Multiplying (1) by 5 and (2) by 2, we get,
`(15)/x - (10)/y` = 0 _________(3)
`(4)/x + (10)/y` = 38 _________(4)
Adding (3) and (4), we get,
`(19)/x` = 38
⇒ x = `(19)/(38)`
= `(1)/(2)`
Now, `(3)/x = (2)/y`
⇒ `(2)/y` = 6
⇒ y = `(2)/(6)`
= `(1)/(3)`
Thus, the solution set is `(1/2, 1/3)`.
Now, y = ax + 3
⇒ `(1)/(3)`
= `(1)/(2)"a" + 3`
⇒ `"a"/(2)`
= `(1)/(3) - 3`
= `(1 - 9)/(3)`
= `(-8)/(3)`
⇒ a = `(-8)/(3) xx 2`
= `(-16)/(3)`
= `-5(1)/(3)`.
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