diff --git a/2024/ruby/day_13.rb b/2024/ruby/day_13.rb
index 1d79604..3416982 100644
--- a/2024/ruby/day_13.rb
+++ b/2024/ruby/day_13.rb
@@ -1,11 +1,4 @@
-require "bundler/inline"
-
-gemfile do
-  source "https://rubygems.org"
-  gem "z3"
-end
-
-require "z3"
+require "matrix"
 
 input = DATA.read
 
@@ -13,16 +6,10 @@ machines = input.split("\n\n")
   .map {|machine| machine.scan(/\d+/).map(&:to_i).each_slice(2).to_a }
 
 def wins(machine)
-  a = Z3.Int("a")
-  b = Z3.Int("b")
-
-  solver = Z3::Solver.new
-  machine.transpose.each do |a_, b_, c|
-    solver.assert a*a_ + b*b_ == c
-  end
-  if solver.satisfiable?
-    model = solver.model
-    [a, b].map { model[_1].to_i }
+  *ab, c = machine
+  a, b = (Matrix.columns(ab).inverse * Matrix.column_vector(c)).to_a.flatten
+  if [a, b].all? { _1.denominator == 1 }
+    [a, b].map(&:to_i)
   else
     nil
   end
@@ -37,16 +24,16 @@ pp machines
 __END__
 Button A: X+94, Y+34
 Button B: X+22, Y+67
-Prize: X=8400, Y=5400
+Prize: X=10000000008400, Y=10000000005400
 
 Button A: X+26, Y+66
 Button B: X+67, Y+21
-Prize: X=12748, Y=12176
+Prize: X=10000000012748, Y=10000000012176
 
 Button A: X+17, Y+86
 Button B: X+84, Y+37
-Prize: X=7870, Y=6450
+Prize: X=10000000007870, Y=10000000006450
 
 Button A: X+69, Y+23
 Button B: X+27, Y+71
-Prize: X=18641, Y=10279
+Prize: X=10000000018641, Y=10000000010279