diff --git a/SCE/SCE/SCE.cpp b/SCE/SCE/SCE.cpp
index 6f9f8d2..8623562 100644
--- a/SCE/SCE/SCE.cpp
+++ b/SCE/SCE/SCE.cpp
@@ -39,6 +39,6 @@ void cylinder()
 void lgs()
 {
 	LGS lgs;
-	lgs.data_entry();
-	cout << lgs.gauss() << endl;
+	//lgs.data_entry();
+	lgs.gauss();
 }
diff --git a/SCE/SCE/lgs.cpp b/SCE/SCE/lgs.cpp
index 1946c1d..8002b99 100644
--- a/SCE/SCE/lgs.cpp
+++ b/SCE/SCE/lgs.cpp
@@ -1,6 +1,8 @@
 #include "lgs.h"
 #include "time.h"
 #include <iostream>
+#include<iostream>
+#include<iomanip>
 using namespace std;
 
 void LGS::data_entry()
@@ -36,6 +38,7 @@ void LGS::data_entry()
 
 void LGS::creat_array()
 {
+	x = new long double[variables];
 	GA = new long double*[variables];
 	for (int i = 0; i < variables; ++i)
 		GA[i] = new long double[variables+1];
@@ -83,50 +86,57 @@ void LGS::print_exp()
 	}
 }
 
+float LGS::gauss()
+{
+	double t1 = clock();
+
+	int i, j, k;
+	data_entry();
+	for (i = 0; i<variables; i++)						//Pivotisation
+		for (k = i + 1; k<variables; k++)
+			if (abs(GA[i][i])<abs(GA[k][i]))
+				for (j = 0; j <= variables; j++)
+				{
+					long double temp = GA[i][j];
+					GA[i][j] = GA[k][j];
+					GA[k][j] = temp;
+				}
+	cout << endl << "Matrix nach Pivot: " << endl;
+	print();
+
+	for (i = 0; i<variables - 1; i++)					//gauss elimination
+		for (k = i + 1; k<variables; k++)
+		{
+			long double t = GA[k][i] / GA[i][i];
+			for (j = 0; j <= variables; j++)
+				GA[k][j] = GA[k][j] - t*GA[i][j];		//make the elements below the pivot elements equal to zero or elimnate the variables
+		}
+
+	cout << endl << "Matrix nach Gausselimination: " << endl;
+	print();
+
+	for (i = variables - 1; i >= 0; i--)                //back-substitution
+	{													//x is an array whose values correspond to the values of x,y,z..
+		x[i] = GA[i][variables];						//make the variable to be calculated equal to the rhs of the last equation
+		for (j = i + 1; j<variables; j++)
+			if (j != i)									//then subtract all the lhs values except the coefficient of the variable whose value is being calculated
+				x[i] = x[i] - GA[i][j] * x[j];
+		x[i] = x[i] / GA[i][i];							//now finally divide the rhs by the coefficient of the variable to be calculated
+	}
+
+	cout << endl << "Loesung: " << endl;
+	for (i = 0; i<variables; i++){
+		int var1 = i + 65;
+		cout << (char)var1 << 1 << " = " << x[i] << endl;							// Print the values of x, y,z,....    
+	}
+	cout << endl;
+
+	return (float)((clock() - t1) / CLOCKS_PER_SEC);
+}
 
 float LGS::cramer()
 {
 	double t1 = clock();
 
 	return (float)((clock() - t1) / CLOCKS_PER_SEC);
-}
-
-float LGS::gauss()
-{
-	double t1 = clock();
-	gauss_down();
-	gauss_up();
-	return (float)((clock() - t1) / CLOCKS_PER_SEC);
-}
-
-void LGS::gauss_down( )
-{
-	for(int stage = 1; stage < variables ; stage++)
-	{
-		long double div = (GA[stage][stage-1] / GA[stage-1][stage-1]);
-		for (int i = 0; i < variables-1 && stage+i < variables; i++)
-		{
-			for (int n = 0; n <= variables; n++)
-			{
-				GA[stage + i][n] = GA[stage + i][n] - (GA[stage - 1][n] * div);
-			}
-
-		}
-
-		print();
-		cout << endl;
-	}
-		
-	
-}
-
-void LGS::gauss_up()
-{
-	
-}
-
-
-
-
-
-
+}
\ No newline at end of file
diff --git a/SCE/SCE/lgs.h b/SCE/SCE/lgs.h
index 35e5fce..7ef9648 100644
--- a/SCE/SCE/lgs.h
+++ b/SCE/SCE/lgs.h
@@ -2,6 +2,7 @@
 class LGS{
 public:
 	long double** GA;
+	long double* x;
 	int variables = 0;
 
 
@@ -11,15 +12,15 @@ public:
 		for (int i = 0; i < variables; ++i)
 			delete[] GA[i];
 		delete[] GA;
+		delete[] x;
 	};
 
-	float gauss();
+	
 	float cramer();
 	void data_entry();
 	void creat_array();
 	void print();
 	void print_ln(int);
 	void print_exp();
-	void gauss_down();
-	void gauss_up();
+	float gauss();
 };
\ No newline at end of file