Solve n linear equations in n unknowns with whole-number coefficients.
Input
A whole number n (1 to 6), then n lines of n + 1 whole numbers: the coefficients of x1 … xn, then the right-hand side.
Output
If there is exactly one solution, n lines x1 = V, x2 = V, …, where each V is a whole number or a fraction in lowest terms such as -3/2. Otherwise print no unique solution.
Examples
Example 1 · Input
2 2 1 5 1 -1 1
Expected output
x1 = 2 x2 = 1
Example 2 · Input
3 2 1 -1 8 -3 -1 2 -11 -2 1 2 -3
Expected output
x1 = 2 x2 = 3 x3 = -1
Prompts inside input() are ignored when checking, so input("n: ") is fine.
Hints
Hint 1
Store every number as a fractions.Fraction so nothing is rounded.
Hint 2
For each column, find a row at or below it with a non-zero entry and swap it up; if there is none, there is no unique solution.
Hint 3
Clear the column in every other row, then x = right side ÷ pivot. str() of a Fraction prints 3/2 or 2.
Solution
Show one correct solution (try it yourself first)
from fractions import Fraction
n = int(input())
rows = [[Fraction(int(x)) for x in input().split()] for _ in range(n)]
unique = True
for col in range(n):
pivot = next((r for r in range(col, n) if rows[r][col] != 0), None)
if pivot is None:
unique = False
break
rows[col], rows[pivot] = rows[pivot], rows[col]
for r in range(n):
if r != col and rows[r][col] != 0:
factor = rows[r][col] / rows[col][col]
rows[r] = [a - factor * b for a, b in zip(rows[r], rows[col])]
if unique:
for i in range(n):
print(f"x{i + 1} = {rows[i][n] / rows[i][i]}")
else:
print("no unique solution")