Question

4m+3n=2. M*n =1/16. Find the value of n=?

Answer 1

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,

\frac{3}{m+n}= \frac{4}{2(m-n)} = \frac{12}{5m-1}

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