find lowest possible x, y and z whole number variables where: x =< 2y+2z 6y =< x+z 3z =< x+y
I am trying to solve this system of 3 linear equations with 3 unknowns and get the ratio that x, y and z have to be in for the inequalities to work. So far I have been able to get a working ratio
Q1 : but I am trying to get a ratio that satisfies the equations below.
x = 2y+2z 6y = x+z 3z = x+y
Q1, a : And if no such ratio exists how can I mathematically determine that?
The formular I used to get a working ratio for the inequality is by solving the equation. I made the equations all equal to each other as follows:
0.5x + x = x + y + z 6y + y = x + y + z 3z + z = x + y + z
This way I was able to get the equation below.
1.5x = 7y = 4z
The equation above satisfies the first inequality but not the corresponding equation.
PS: I am not very conversant with the tags if I have left any out please add. Thank you.