The number of non-negative integer solutions of the equations 6   x + 4   y + z = 200 and x + y + z = 100 100 is

Step-by-step solution

Given equations 6   x + 4   y + z = 200 and x + y + z = 100 By Eqs. (i) and (ii), we get 5   x + 3   y = 100   For non-negative integer solutions, when x = 2  then  y = 30 x = 5 ,  then  y = 25 x = 8  then  y = 20 x = 11 ,  then  y = 15 x = 14 ,  then  y = 10 x = 17 ,  then  y = 5 and x = 20 , then y = 0 In every case z = 100 - ( x + y ) > 0 So, total number of non-negative integral solutions are 7 .