Like Model Test Papers4699. Find the values of m and n for which the f

1.	Like Model Test Papers4699. Find the values of m and n for which the following system of linear equations has infimitelymany solutions:3x+4y12(m + n)x + 2(m-n)y = (5m-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, 3/(m+n)= 4/2(m-n) = 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

Like Model Test Papers4699. Find the values of m and n for which the following system of linear equations has infimitelymany solutions:3x+4y12(m + n)x + 2(m-n)y = (5m-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,

3/(m+n)= 4/2(m-n) = 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