Solving Simultaneous Equations in C#: A Junior Secondary Guide
Welcome to this junior secondary C# math project! In this tutorial, you'll learn how to
solve simultaneous equations with three unknowns using C#.
This is a great way to combine your coding skills with algebra and logic.
You'll also learn the following:
- How to use C# to solve 3x3 simultaneous equations
- Applying the elimination method step-by-step
- Using LCM (Least Common Multiple) to simplify equations
- Writing a C# class to automate the solving process
How to Solve Three-Variable Algebra Problems | Maths Explanation for C# Kids
To solve 3 by 3 simultaneous equations, we will simply eliminate the z variable, then call out to our C# Code for Simultaneous Equations with 2 Unknowns module.
Step-by-Step Guide to Solve Three-Variable Algebra Equations | Elimination Method C# Algorithm
Let's try to draft a C# algorithm that solves simultaneous equations with 2 unknowns,
using the elimination method, with the following set of equations in consideration.
x + 2y - z = 2; and
3x - y + 2z = 4
2x + 3y + 4z = 9
These steps will help the student understand both the math and the logic behind the code.
Step 1:
Using the Find LCM in C#
class from the Primary Category, find the LCM of the coefficients of variable z.
Multiply equations 1, 2 & 3 by the LCM of the coefficients
of variable z, divided by the z coefficient
of the respective equation.
(4/-1) X (x + 2y - z = 2)
⇒
-4x - 8y + 4z = -8
(4/2) X (3x - y + 2z = 4)
⇒
6x - 2y + 4z = 8
(4/4) X (2x + 3y + 4z = 9)
⇒
2x + 3y + 4z = 9
Step 2:
Subtract the new equations obtained in Step 2;
eqn (2) from eqn (1) and eqn (3) from eqn (2).
-4x - 8y + 4z = -8
-
6x - 2y + 4z = 8
⇒
-10x - 6y = -16
6x - 2y + 4z = 8
-
2x + 3y + 4z = 9
⇒
4x - 5y = -1
Step 3:
Call out to our C# Code for Simultaneous Equations with 2 Unknowns
module to solve for x and y.
⇒
(x, y) = (1, 1);
Step 4:
Obtain z by solving for z from any of the
original equations, using the found values of x
and y.
x + 2y - z = 2
⇒
1 + 2(1) - z = 2;
⇒
-z = 2 - 3 = -1;
⇒
z = -1/-1 = 1;
Create a new C# class file;
call it Simultaneous3Unknown.
Type out the adjoining C# code for solving simultaneous equations with 3 unknowns.
Note: The code module for
finding LCM in C#
has been explained in the Primary Category.
You can comment out the Simultaneous2Unknown C# object
code in the main class from the previous lesson or simply continue from where it stopped.
So! C# Fun Practice Exercise - Simultaneous Equations with 3 Unknowns
As a fun practice exercise, feel free to try out your own set of x_coefficients, y_coefficients and equals values, and see how the C# code solves the resulting 3x3 Simultaneous Equations.
C# Code for Solving Simultaneous Equations with 3 Unknowns - Class File
using System.Collections.Generic;
namespace Algebra
{
class Simultaneous3Unknown
{
private int[] x_coefficients;
private int[] y_coefficients;
private int[] z_coefficients;
private int[] equals;
private double[,] eliminator;
private double x_variable;
private double y_variable;
private double z_variable;
public Simultaneous3Unknown(int[] x_coeff, int[] y_coeff, int[] z_coeff, int[] eq)
{
x_coefficients = new int[] { x_coeff[0], x_coeff[1], x_coeff[2] };
y_coefficients = new int[] { y_coeff[0], y_coeff[1], y_coeff[2] };
z_coefficients = new int[] { z_coeff[0], z_coeff[1], z_coeff[2] };
equals = new int[] { eq[0], eq[1], eq[2] };
eliminator = new double[3, 3];
}
public double[] solveSimultaneous()
{
int lcm;
List<int> stooge = new List<int>();
foreach (int z in z_coefficients)
{
stooge.Add(Math.Abs(z));
}
LCM l_c_m = new LCM(stooge);
lcm = l_c_m.getLCM();
// STEP 1:
eliminator[0, 0] = (lcm * x_coefficients[0]) / z_coefficients[0];
eliminator[0, 1] = (lcm * y_coefficients[0]) / z_coefficients[0];
eliminator[0, 2] = (lcm * equals[0]) / z_coefficients[0];
eliminator[1, 0] = (lcm * x_coefficients[1]) / z_coefficients[1];
eliminator[1, 1] = (lcm * y_coefficients[1]) / z_coefficients[1];
eliminator[1, 2] = (lcm * equals[1]) / z_coefficients[1];
eliminator[2, 0] = (lcm * x_coefficients[2]) / z_coefficients[2];
eliminator[2, 1] = (lcm * y_coefficients[2]) / z_coefficients[2];
eliminator[2, 2] = (lcm * equals[2]) / z_coefficients[2];
// STEP 2:
double[] new_x = {
eliminator[0, 0] - eliminator[1, 0],
eliminator[1, 0] - eliminator[2, 0]
};
double[] new_y = {
eliminator[0, 1] - eliminator[1, 1],
eliminator[1, 1] - eliminator[2, 1]
};
double[] new_eq = {
eliminator[0, 2] - eliminator[1, 2],
eliminator[1, 2] - eliminator[2, 2]
};
try
{
// STEP 3:
double[] partial_solution;
partial_solution = (new Simultaneous2Unknown(new_x, new_y, new_eq)).solveSimultaneous();
x_variable = partial_solution[0];
y_variable = partial_solution[1];
// STEP 4:
z_variable = (equals[0] - x_coefficients[0] * x_variable - y_coefficients[0] * y_variable) / z_coefficients[0];
}
catch (Exception e)
{
throw e;
}
return new double[] { x_variable, y_variable, z_variable };
}
}
}
C# Code for Solving Simultaneous Equations with 3 Unknowns - Main Class
using System.Collections.Generic;
namespace Algebra
{
class Program
{
static void Main(string[] args)
{
Console.WriteLine("Welcome to our demonstration sequels");
Console.WriteLine("Hope you enjoy (and follow) the lessons.");
Console.WriteLine("\r\n");
/*
* Simultaneous Equations with 3 unknowns
*/
char[, ] operate = new char[3, 2];
double[] result3D;
int[] x_coeff = new int[] { 2, 4, 2 };
int[] y_coeff = new int[] { 1, -1, 3 };
int[] z_coeff = new int[] { 1, -2, -8 };
int[] equals = new int[] { 4, 1, -3 };
for (int i = 0; i < 3; i++)
{
operate[i, 0] = '+'; // lazy if..else
if (y_coeff[i] < 0)
{
operate[i, 0] = '-';
}
operate[i, 1] = '+';
if (z_coeff[i] < 0)
{
operate[i, 1] = '-';
}
}
Console.WriteLine("\r\n Solving simultaneously the equations:\r\n");
//Print as an equation
Console.WriteLine(String.Format("{0,20}x {1} {2}y {3} {4}z = {5}",
x_coeff[0], operate[0, 0], Math.Abs(y_coeff[0]),
operate[0, 1], Math.Abs(z_coeff[0]), equals[0]
)
);
Console.WriteLine(String.Format("{0,20}x {1} {2}y {3} {4}z = {5}",
x_coeff[1], operate[1, 0], Math.Abs(y_coeff[1]),
operate[1, 1], Math.Abs(z_coeff[1]), equals[1]
)
);
Console.WriteLine(String.Format("{0,20}x {1} {2}y {3} {4}z = {5}",
x_coeff[2], operate[2, 0], Math.Abs(y_coeff[2]),
operate[2, 1], Math.Abs(z_coeff[2]), equals[2]
)
);
Console.WriteLine(Environment.NewLine);
Console.Write(String.Format("{0,15} {1}{2,20}", "Yields:", "\r\n", "(x, y, z) = "));
try
{
Simultaneous3Unknown sim3unk;
sim3unk = new Simultaneous3Unknown(x_coeff, y_coeff, z_coeff, equals);
result3D = sim3unk.solveSimultaneous();
Console.Write(String.Format("({0:0.0000}, {1:0.0000}, {2:0.0000})", result3D[0], result3D[1], result3D[2]));
}
catch (Exception)
{
Console.Write("(infinity, infinity, infinity)");
}
}
}
}