How many positive integral solutions can you find to this system of equations?
x1+x2=8
x2-x3=-3
x3+x4=14
x4-x5=-5
x5+x6=18
x6-x7=4
x7-x8=-3
Note:
1)xi>=1.
2)Neither I nor Shivanker could find a simple enough solution for this problem. Can you come up with the awesome and simple solution?
Note: x1,x2,x3,...,x8 are all variables
ReplyDeletex1=5,4,3,2,1
ReplyDeletex2=3,4,5,6,7
x3=6,7,8,9,10
x4= 4,5,6,7,8
x5= 13,12,11,10,9
x6= 5,6,7,8,9
x7= 1,2,3,4,5
x8= 4,5,6,7,8
RESPECTIVELY
(i have tried to make a grid above.it is a column row arrgangement.i have written it in short)
i.e, x1=5
x2=3
x3=6
x4=4
x5=13
x6=5
x7=1
x8=4
is the 1st set of solution.like column row arrangement.each column corresponds to a set of solution
so there are 5 sets of solutions
same as rohin and not able to find shortcut
ReplyDelete1<=x1<=7
ReplyDelete1<=x2<=7
4<=x3<=10
4<=x4<=10
9<=x5<=15
3<=x6<=9
-1<=x7<=5 but we know min is 1 therefore, new inequality is 1<=x7<=5
4<=x1<=8 new inequality
from this we can clearly conclude only 5 possible sets are possible 1<=x7<=5