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Question
If the following three equations hold simultaneously for x and y, find the value of 'm'.
2x + 3y + 6 = 0
4x - 3y - 8 = 0
x + my - 1 = 0
Solution
The given equations are
2x + 3y + 6 = 0 ....(i)
4x - 3y - 8 = 0 ....(ii)
x + my - 1 = 0 ....(ii)
Adding eqns. (i) and (ii), we get
6x - 2 = 0
⇒ 6x = 2
⇒ x = `(1)/(3)`
Substituting the value of x in eqn. (i), we get
`2 xx (1)/(3) + 3y + 6` = 0
⇒ 3y
= `-6 - (2)/(3)`
= `(18 - 2)/(3)`
= `(-20)/(3)`
⇒ y = `-(20)/(9)`
Substituting the value of x and in eqn. (iii), we get
`(1)/(3) + "m" xx (-20/9) - 1` = 0
⇒ `-(20)/(9)"m"`
= `1 - (1)/(3)`
= `(2)/(3)`
⇒ m
= `-(2)/(3) xx (9)/(20)`
= `-(3)/(10)`.
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