#include <algorithm>
#include <iostream>
#include <array>

int main() {

    std::array<unsigned int, 5> bin_combinations = {1, 1, 0, 0, 0};
    double A[2][5] = {
            {1.0, 0.0, 1.0, -1.0, 2.0},
            {0.0, 1.0, -1.0, 2.0, -1.0}
    };
    double b[] = {2.0, 1.0};


    do {
        unsigned int tmp[2];

        size_t pos_tmp = 0;
        for (int i = 0; i != bin_combinations.size(); ++i)
            if (bin_combinations[i])
                tmp[pos_tmp++] = i;

        size_t x1 = tmp[0], x2 = tmp[1];

        double tA[2][2];
        double tb[2];

        bool key = true;

        if (A[0][x1] == 0)
            key = !key;

        for (int row = 0; row != 2; ++row) {
            tA[row][x1] = A[row][key ? x1 : x2];
            tA[row][x2] = A[row][key ? x1 : x2];
            tb[row] = b[key? row : 1 - row];
        }


        tb[0] /= tA[0][0];
        tA[0][1] = tA[0][1] / tA[0][0];
        tA[0][0] = tA[0][0] / tA[0][0];

        if (tA[1][0] != 0) {
            double k;
            k = tA[1][0] / tA[0][0];
            tA[1][0] -= k * tA[0][0];
            tA[1][1] -= k * tA[0][1];
            tb[1] -= tb[0] * k;
        }

        if (tA[1][1] != 0) {
            double k;

            tb[1] /= tA[1][1];
            tA[1][1] /= tA[1][1];

            k = tA[0][1] / tA[1][1];
            tA[0][1] -= k * tA[1][1];
            tb[0] -= k * tb[1];
        }

        std::cout << "x" << x1 << ": " << tb[0] << ", x" << x2 << ": " << tb[1] << std::endl;

    } while(std::prev_permutation(bin_combinations.begin(), bin_combinations.end()));

    return 0;
}