Question

Find the values of m and n for which the following system of linear equations has infinitely many solutions 3x+4y=12 (m+n)x + 2(m-n)y = (5m-1)

Answer 1

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Answer 2

Given :   system of linear equations 3x+4y=12 (m+n)x + 2(m-n)y = (5m-1) with infinite solutions

To find : Value of m & n

Solution:

linear equations has infinitely many solutions

(m+n)x + 2(m-n)y = (5m-1)

3x+4y=12

=> (m + n)/3  = 2(m-n)/4  = (5m - 1)/12

(m + n)/3  = 2(m-n)/4

=>  (m + n)/3  =  (m-n)/2

=>  2m + 2n = 3m - 3n

=> m = 5n

(m + n)/3    = (5m - 1)/12

=>  4(m + n)    = (5m - 1)

=> 4m + 4n = 5m - 1

=> m = 4n + 1

=> 5n = 4n+ 1

=> n  = 1

=> m = 5

m = 5  , n = 1

m = 5  , n = 1  linear equations has infinitely many solutions  

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