Question

The value of expression mx - ny is 3 when x = 5 and y = 6. And its value is 8 when x = 6 and y = 5. Find the values of m and n.

Answer 1

The value of expression mx - ny is 3 when x = 5 and y = 6.
⇒ 5m - 6n = 3                              .....(1)

The value of expression mx - ny is 8 when x = 6 and y = 5.
⇒ 6m - 5n = 8                              ....(2)

Multiply equation (1) by 6 and equation (2) by 5, We get:
30m - 36n = 18                            ....(3)
30m - 25n = 40                            .....(4)

Subtracting equation (4) from (3)
   30m - 36n = 18
-  30m - 25n = 40 
    -       +        -     
           - 11n = - 22
                 n = 2
Substituting n = 2 in equation (1), we get
5m - 6(2) = 3
⇒ 5m = 15
⇒ m = 3
∴ Solution is m = 3 and n = 2.