5. Find the value of mand n for which the following system of linear e

1.	5. Find the value of mand n for which the following system of linear equations has infinitely manysolution3x + 4y = 12(m + n)x + 2(m n )y = 5m - 1
Answer» If equations3x + 4y = 12(m+n)x + 2(m-n)y = 5m - 1 Have infinitely many solutionsThen,3/(m+n) = 4/2(m-n) = 12/(5m-1) 6(m - n) = 4(m + n)6m - 4m = 4n + 6n2m = 10nm = 5n.......(1) 3(5m-1) = 12(m+n)5m - 1 = 4m + 4n5m - 4m = 4n + 1m = 4n + 1......(2) Put value of m from eq(1) in eq(2)5n = 4n + 15n - 4n = 1n = 1 m = 4*1 + 1 = 5 Therefore, Value of m = 5, n = 1

5. Find the value of mand n for which the following system of linear equations has infinitely manysolution3x + 4y = 12(m + n)x + 2(m n )y = 5m - 1

Answer»

If equations3x + 4y = 12(m+n)x + 2(m-n)y = 5m - 1

Have infinitely many solutionsThen,3/(m+n) = 4/2(m-n) = 12/(5m-1)

6(m - n) = 4(m + n)6m - 4m = 4n + 6n2m = 10nm = 5n.......(1)

3(5m-1) = 12(m+n)5m - 1 = 4m + 4n5m - 4m = 4n + 1m = 4n + 1......(2)

Put value of m from eq(1) in eq(2)5n = 4n + 15n - 4n = 1n = 1

m = 4*1 + 1 = 5

Therefore, Value of m = 5, n = 1