Question

Find the value of m and n
3x+4y=12
(m+n)x + 2(m-n)=5m-1
Provided the eqn has infinite solutions

Answer 1

Answer:

If two linear equations have infinitely many solutions means

a1/a2 = b1/b2 = c1/c2

here two linear equations are

3x+4y=12  and (m+n)x + 2(m-n)y = (5m-1)  

So we can write,

= =

From this we get, 3/(m+n) = 4/[2(m-n)]

                          6(m-n)=4(m+n)

                          6m - 6n = 4m -4n

                          2m - 10n = 0 --------------(1)

similarly      3/(m+n) = 12/(5m-1)

                3m - 12n = 3 -------------------(2)

(1)    ⇒ 6m - 30n=0 -------(3)

(2)   ⇒  6m - 24n = 6 ------(4)

(4) - (2)  ⇒ 6n = 6

              n = 1

substituting the value of n in (1)

then (1)  becomes 2m - 10 =0

           m=5

Therefore m= 5 and n=1