a + b = 160
a + c = 150
b + d = 140
d + c = 130

a+b+0c+0d=160
a+0b+c+0d=150
0a+b+0c+1d=140
0a+0b+c+d=130

1 1 0 0 160
0 -1 1 0 -10
0 0 1 1 130
0 0 1 1 130
rank<4

it seems an infinite solution set