Since you want the least average, then you want the most amount of small numbers
There has to be a 5.5 median so the list would have to have one 5 and one 6.
so the list would be 1,2,3,4,5,6,7,8,9,10 since there cannot be reapeats
1+2+3+4+5+6+7+8+9+10 is 11* 5 since 1+10 is 11 2+9 is 11...
so the average is 55/10 or 5.5
I think the answer is 12/19
To get no solutions the variable side must cancel out.
Since the last equation only has variables x and z, we have to cancel the y so
Multiply x+y+3z=10 by 8 to get 8x+8y+24z=80
substract the second equation to get 12x+19z=63
then we have to cancel the z
multiply the last equation by 19 to get 19xz+19z=57
(12x+19z=63)-(19xk+19z=57) to get 12x-19xk=6
the left side of the equation must equal zero, so 12x=19xk
divide by 19