Question

If x = 2 and y = 3 is the unique solution of pair of linear euation mx − 4y + 3 = 0 and 3x + ny + 4 = 0.then find the value of m and n.

Answer 1

Answer :

m = 9/2 , n = -10/3

Solution :

Here ,

The given linear equations are ;

mx - 4y + 3 = 0 -------(1)

3x + ny + 4 = 0 -------(2)

Also ,

It is given that , x = 2 and y = 3 is the unique solution of the given pair of linear equations , thus x = 2 and y = 3 must satisfy both the equations simultaneously .

Now ,

Putting x = 2 and y = 3 in eq-(1) , we get ;

=> mx - 4y + 3 = 0

=> m•2 - 4•3 + 3 = 0

=> 2m - 12 + 3 = 0

=> 2m - 9 = 0

=> 2m = 9

=> m = 9/2

Also ,

Putting x = 2 and y = 3 in eq-(1) , we get ;

=> 3x + ny + 4 = 0

=> 3•2 + n•3 + 4 = 0

=> 6 + 3n + 4 = 0

=> 3n + 10 = 0

=> 3n = -10

=> n = -10/3

Hence ,

m = 9/2 , n = -10/3