#include<iostream>
using namespace std;

int n;		//未知數(shù)的個(gè)數(shù)
double a[100][100];		//系數(shù)矩陣的增廣矩陣
double x[100];		//解向量x

void main()
{
	int i, j;		//循環(huán)變量
	double m;		//系數(shù)
	cout << "請輸入未知數(shù)的個(gè)數(shù)n：";
	cin >> n;
	cout << "請輸入系數(shù)矩陣的增廣矩陣：" << endl;
	//輸入矩陣
	for(i = 1; i <= n; i ++){
		for(j = 1; j <= n+1; j ++){
			cin >> a[i][j];
		}
	}

	//Gauss_Jordan消元
	for(i = 1; i <= n; i ++){
		for(j = 1; j <=n; j ++){	//對于每一行都進(jìn)行消元，則可消成對角矩陣
			if(j == i) continue;	//跳過本身這一行
			m = a[j][i] / a[i][i];	//計(jì)算系數(shù)
			for(int k = 1; k <= n+1; k ++){		//E[j] - m*E[i] -> E[j]
				a[j][k] = a[j][k] - m * a[i][k];
			}
		}
	}
	//如果最后一行為0，則沒有惟一解
	if(a[n][n] == 0){
		cout << "no unique solution exists." << endl;
		return;
	}
	//計(jì)算每一個(gè)未知數(shù)x[i]的值
	for(i = 1; i <= n; i ++){
		x[i] = a[i][n+1] / a[i][i];
		cout << "x" << i << " = " << x[i] << endl;
	}
}