高斯消元求解线性方程组，详见高斯消元法详解

C++ 代码

/* 
 * @Author: lzyws739307453 
 * @Language: C++ 
 */
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 105;
const double eps = 1e-8;
double a[MAXN][MAXN];
int Select(double a[][MAXN], int n) {
    int r = 1;
    for (int c = 1; c <= n; c++) {
        int t = r;
        for (int i = r + 1; i <= n; i++)
            if (fabs(a[i][c]) > fabs(a[t][c]))
                t = i;
        if (fabs(a[t][c]) < eps)//无解或无穷多解
            continue;
        if (t != r)
            for (int i = c; i <= n + 1; i++)
                swap(a[r][i], a[t][i]);
        for (int i = n + 1; i >= c; i--)
            a[r][i] /= a[r][c];
        for (int i = r + 1; i <= n; i++)
            if (fabs(a[i][c]) > eps)
                for (int j = n + 1; j >= c; j--)
                    a[i][j] -= a[r][j] * a[i][c];
        r++;
    }
    return r;
}
int Gauss(double a[][MAXN], int n) {
    int r = Select(a, n);
    if (r <= n) {
        for (int i = r; i <= n; i++)
            if (fabs(a[i][n + 1]) > eps)
                return 0;//无解
        return 2;//无穷多解
    }
    for (int i = n; i >= 1; i--)
        for (int j = i + 1; j <= n; j++)
            a[i][n + 1] -= a[i][j] * a[j][n + 1];
    return 1;//有唯一解
}
int main() {
    int n;
    scanf("%d", &n);
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= n + 1; j++)
            scanf("%lf", &a[i][j]);
    int Judge = Gauss(a, n);
    if (!Judge)
        printf("No solution\n");
    else if (Judge > 1)
        printf("Infinite group solutions\n");
    else {
        for (int i = 1; i <= n; i++)
            printf("%.2f\n", a[i][n + 1]);
    }
    return 0;
}