Understanding Linear Algebra Systems | Maths Explanation for Visual Basic Kids
Welcome to this beginner-friendly Visual Basic tutorial designed for junior secondary students learning algebra.
Visual Basic is a great tool for solving math problems. It helps students visualize and automate algebraic solutions. This tutorial is perfect for:
- Junior secondary students learning Visual Basic
- Teachers looking for math coding projects
- Anyone curious about solving equations with code
In this lesson, you'll discover how to solve simultaneous equations with two unknowns using Visual Basic.
We'll walk through the elimination method and show you how to write a simple Visual Basic script to solve linear systems.
The resulting algorithm solves the linear system using basic algebra and Visual Basic logic.
It's ideal for school projects and math exercises.
Well, it hasn't been much of algebra in our junior secondary school Visual Basic tutorial series so far; We are about to have our first taste of it.
What Are Simultaneous Equations? | Maths Explanation for Visual Basic Kids
Simultaneous equations are a set of equations with multiple variables that are solved together. For example:
2x + 3y = 13; and
5x - y = 7
Simultaneous equations can be solved using algebraic methods like Substitution or Elimination,
or advanced methods like Matrix and Cramer's Rule.
In this tutorial, we'll focus on the elimination method and implement it using Visual Basic.
Step-by-Step Guide to Solve Simultaneous Equations with 2 Unknowns | Elimination Method Visual Basic Algorithm
Let's try to draft a Visual Basic algorithm that solves simultaneous equations with 2 unknowns,
using the elimination method, with the following set of equations in consideration.
2x + 3y = 13; and
5x - y = 7
Step 1:
Pick a variable to eliminate, either x or y.
Our code will always eliminate the y variable.
Step 2:
Multiply equation 1 by the coefficient of variable y
in equation 2.
⇒
-1 X (2x + 3y = 13)
⇒
-2x - 3y = -13
Step 3:
Multiply equation 2 by the coefficient of variable y
in equation 1.
⇒
3 X (5x - y = 7)
⇒
15x - 3y = 21
Step 4:
Subtract the new equations obtained from Steps 2 and 3.
-2x - 3y = -13
-
15x - 3y = 21
⇒
-17x = -34
Step 5:
Divide the R.H.S. from Step 4 by the coefficient of
x to obtain x.
⇒
x = -34/-17 = 2;
Step 6:
Obtain y by solving for y from any of the
original equations, using the found value of x.
2x + 3y = 13
⇒
2(2) + 3y = 13;
⇒
3y = 13 - 4 = 9;
⇒
y = 9/3 = 3;
Create a new VB.Net class file; Project, Add Class.
Call it Simultaneous2Unknown.vb.
Optionally, Create a new VB.Net module file; Project, Add Module.
Call it Simultaneous2UnknownModule.vb.
Type out the adjoining Visual Basic (VB.Net) codes for solving simultaneous equations with 2 unknowns.
Note: You can instead comment out the VB.Net code in
the main module from the previous lesson or simply continue from where it stopped.
So! Visual Basic Fun Practice Exercise - Simultaneous Equations with 2 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 Visual Basic code solves the resulting 2 by 2 Simultaneous Equations.
VB.Net Code for Solving Simultaneous Equations with 2 Unknowns - Class File
Public Class Simultaneous2Unknown
Dim x_coefficients() As Double
Dim y_coefficients() As Double
Dim equal() As Double
Dim eliminator(1, 1) As Double
Dim x_variable As Double
Dim y_variable As Double
Public Sub _init_(equations As Dictionary(Of String, Double()))
x_coefficients = equations("x")
y_coefficients = equations("y")
equal = equations("eq")
End Sub
Public Function solveSimultaneous() As Double()
eliminator(0, 0) = y_coefficients(1) * x_coefficients(0)
eliminator(0, 1) = y_coefficients(1) * equal(0)
eliminator(1, 0) = y_coefficients(0) * x_coefficients(1)
eliminator(1, 1) = y_coefficients(0) * equal(1)
Try
x_variable = (eliminator(0, 1) - eliminator(1, 1)) / (eliminator(0, 0) - eliminator(1, 0))
y_variable = (equal(0) - x_coefficients(0) * x_variable) / y_coefficients(0)
Return {x_variable, y_variable}
Catch ex As DivideByZeroException
Throw ex
Return Nothing
End Try
End Function
End Class
VB.Net Code for Solving Simultaneous Equations with 2 Unknowns - Main Module
Module Algebra_Simultaneous2Unknown
Sub Main()
Dim operators As String() = {"+", "+"}
Dim x_coefficients As Double() = {8.0, 2.0}
Dim y_coefficients As Double() = {-5.0, 17.0}
Dim equal As Double() = {89.0, 150.0}
Dim equations As New Dictionary(Of String, Double())
equations.Add("x", x_coefficients)
equations.Add("y", y_coefficients)
equations.Add("eq", equal)
If y_coefficients(0) < 0 Then
operators(0) = "-"
End If
If y_coefficients(1) < 0 Then
operators(1) = "-"
End If
Console.WriteLine(vbCrLf, " Solving simultaneously the equations:", vbCrLf)
Console.WriteLine(String.Format("{0,20}x {1} {2}y = {3}",
x_coefficients(0), operators(0), Math.Abs(y_coefficients(0)), equal(0)
)
)
Console.WriteLine(String.Format("{0,20}x {1} {2}y = {3}",
x_coefficients(1), operators(1), Math.Abs(y_coefficients(1)), equal(1)
)
)
Console.WriteLine(Environment.NewLine)
Console.Write(String.Format("{0,15} {1}{2,20}", "Yields:", vbCrLf, "(x, y) = "))
Try
Dim sim2unk As New Simultaneous2Unknown
sim2unk._init_(equations)
Dim solution = sim2unk.solveSimultaneous()
Console.Write(String.Format("({0:0.0000}, {1:0.0000})", solution(0), solution(1)))
Catch ex As Exception
Console.Write("(infinity, infinity)")
End Try
End Sub
End Module
