>>229 Ruby
s = ->a, b{a.zip(b).map{|i, j| i - j}}
t = ->a, k{a.map{|i| i * k}}
n = gets.to_i - 1
m = $<.read.split($/).map{|e| f[n, *e.split.map(&:to_r)]}
(1..n+1).each do |r|
(nonzero = m[r- 1..-1].find_index{|e| e[r].nonzero?} + r - 1) && next
m[r - 1], m[nonzero] = m[nonzero], m[r - 1]
m[r - 1] = t[m[r - 1], 1/m[r - 1][r]]
[*[*(0..n)] - [r - 1]].each{|i| m[i] = s[m[i], t[m[r - 1], m[i][r]/m[r - 1][r]]]}
end
puts m.transpose[0].map{|i| i.denominator == 1 ? i.to_i : i} * ' '

2
0 1
1 3
#=> 2 1 (y=2x+1)

3
1 1 1 1
5 4 2 1
8 9 3 1
#=> -1/2 11/2 -4