#include <fstream>
#include <iostream>
#include <iomanip>
#include <cmath>

enum { kSize = 3 };

typedef double SqMatT[][kSize];

void Dump(std::ostream& o, double const v[kSize])
{
    for (int i = 0; i < kSize; ++i)
    {
        o << v[i] << '\t';
    }
    o << std::endl;
}

void Dump(std::ostream& o, SqMatT const m)
{
    for (int i = 0; i < kSize; ++i)
    {
        Dump(o, m[i]);
    }
}


void Eliminate(SqMatT a, double b[])
{
    int n = kSize;
    for (int i = 0; i < n -1; ++i)
    {
        for (int j = i + 1; j < n; ++j)
        {
            double c = a[j][i] / a[i][i];
            for (int k = i; k < n; ++k)
            {
                a[j][k] -= c * a[i][k];
            }
            b[j] -= c * b[i];
        }
    }
}


void BackSubstitute(SqMatT U, double const c[], double x[])
{
    for (int i = kSize - 1; 0 <= i; --i)
    {
        double s = 0.;
        for (int j = i + 1; j < kSize; ++j)
        {
            s += U[i][j] * x[j];
        }
        x[i] = (c[i] - s)/U[i][i];
    }
}


int main()
{
    SqMatT m =
    {
        {  2,  3,  0, },
        {  0,  1,  0, },
        {  0,  5,  1, },
    };

    double b[kSize] = { 2, 3, 4, };

    Eliminate(m, b);

    double x[kSize];
    BackSubstitute(m, b, x);

    //std::ofstream o("jjj.tsv");
    Dump(std::cout, x);
}

-3.5	3	-11