Question

Please explain this solution

Answer 1

Step-by-step explanation:

It is a Linear equations

It is telling that 2n+4m=mn

means that we have to like reciprocal it

mn-2n=4m

n(m-2)=4m

now we have to divide it

and we say the number n we have to find it out

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Answer 2

Given : 1/m  +  2/n    = 1/2   m , n are integers

To find : Ordered pairs of m & n

Solution:

1/m  +  2/n    = 1/2

multiplying  by 2mn both sides

=> 2n + 4m  =  mn

=> n(m - 2)  = 4m

=> n = 4m/(m - 2)

=> n = (4m - 8 + 8)/(m - 2)

=> n = (4m-8)/(m - 2)   + 8/(m-2)

=> n = 4  +   8/(m-2)

n & m are integers

=> 8/(m - 2)   should be integer

8 = 1 * 8  or  2 * 4  or (-1)(-8)  or (-2)(-4)

=> m-2   can be   ±1   , ±2   , ±4  or  ±8

m -2  = -1 => m = 1

m -2 = 1 => m = 3

m -2 = - 2 => m = 0   can not be zero  as 1/0 not defined

m - 2 = 2  => m = 4

m - 2 = -4 => m = - 2

m - 2 = 4 => m = 6

m -2 = -8  => m = -6

m - 2 = 8 => m = 10

=> m =  1  , 3   , 4 ,    - 2 , 6  , -6  , 10  

now using  n = 4  +   8/(m-2)

put values of m to get value of n

m =  -6    ,  -2  , 1 ,  3  , 4   ,  6  , 10

n =    3   ,  2   , -4  , 12 , 8  ,  6  ,  5

ordered pairs = (-6 , 3)  (-2 , 2) , ( 1, -4) ( 3, 12) , (4 , 8) , (6 , 6) , ( 10 , 5)

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