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

Answer 1

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)`.