Simultaneous Equation Solver | Visual Basic Sample Code

Solving Simultaneous Equations

Simultaneous equations are equations that involve two or more unknown variables. There must be as many equations as the number of unknown variables to solve the system.

Linear simultaneous equations take the following forms:

Equation 1: ax + by = m

Equation 2: cx + dy = n

There are two common methods to solve simultaneous equations: substitution and elimination. This solver uses the substitution method with the following formulas:

x = (b * n - d * m) / (b * c - a * d)

y = (a * n - c * m) / (a * d - b * c)

Try the interactive calculator below to solve your equations:

Interactive Equation Solver

Division by zero! The equations are dependent or inconsistent.

Equation 1

a:

b:

=

Equation 2

c:

d:

=

Solution for x

-

Solution for y

-

Your Equations

2x + 3y = 8

4x - y = 6

Visual Basic Code Examples

VB6 Implementation

This VB6 code solves simultaneous equations using the substitution method:

Private Sub Solve_Click()
    Dim a, b, c, d, m, n As Double
    Dim x, y As Double
    
    ' Get coefficients from textboxes
    a = Val(Txt_a.Text)
    b = Val(Txt_b.Text)
    m = Val(Txt_m.Text)
    c = Val(Txt_c.Text)
    d = Val(Txt_d.Text)
    n = Val(Txt_n.Text)
    
    ' Calculate denominator
    Dim denominator As Double
    denominator = (b * c - a * d)
    
    ' Check for division by zero
    If denominator = 0 Then
        MsgBox "Equations are dependent or inconsistent!", vbExclamation
        Exit Sub
    End If
    
    ' Calculate solutions
    x = (b * n - d * m) / denominator
    y = (a * n - c * m) / (a * d - b * c)
    
    ' Display results rounded to 2 decimal places
    Lbl_x.Caption = Round(x, 2)
    Lbl_y.Caption = Round(y, 2)
End Sub

Private Sub New_Click()
    ' Clear all input fields and results
    Txt_a.Text = ""
    Txt_b.Text = ""
    Txt_m.Text = ""
    Txt_c.Text = ""
    Txt_d.Text = ""
    Txt_n.Text = ""
    Lbl_x.Caption = ""
    Lbl_y.Caption = ""
End Sub

VB.NET Implementation

Modern VB.NET implementation with error handling:

Public Class EquationSolver

    Private Sub btnSolve_Click(sender As Object, e As EventArgs) Handles btnSolve.Click
        Dim a, b, c, d, m, n As Double
        Dim x, y As Double
        
        ' Validate and parse inputs
        If Not Double.TryParse(txtA.Text, a) Or
           Not Double.TryParse(txtB.Text, b) Or
           Not Double.TryParse(txtM.Text, m) Or
           Not Double.TryParse(txtC.Text, c) Or
           Not Double.TryParse(txtD.Text, d) Or
           Not Double.TryParse(txtN.Text, n) Then
            
            MessageBox.Show("Please enter valid numbers", "Input Error")
            Return
        End If
        
        Dim denominator As Double = b * c - a * d
        
        ' Check for division by zero
        If Math.Abs(denominator) < 0.000001 Then
            MessageBox.Show("Equations are dependent or inconsistent", "Calculation Error")
            Return
        End If
        
        ' Calculate solutions
        x = (b * n - d * m) / denominator
        y = (a * n - c * m) / (a * d - b * c)
        
        ' Display results with formatting
        lblX.Text = Math.Round(x, 4).ToString()
        lblY.Text = Math.Round(y, 4).ToString()
    End Sub

    Private Sub btnReset_Click(sender As Object, e As EventArgs) Handles btnReset.Click
        ' Clear all inputs and results
        txtA.Clear()
        txtB.Clear()
        txtM.Clear()
        txtC.Clear()
        txtD.Clear()
        txtN.Clear()
        lblX.Text = ""
        lblY.Text = ""
    End Sub
End Class

How the Solver Works

Mathematical Foundation

The solver uses algebraic elimination to find solutions for the system of equations.

Error Handling

Checks for division by zero which occurs with dependent or inconsistent equations.

VB Implementation

Shows both VB6 and modern VB.NET approaches with proper validation.

Interactive Demo

Real-time equation solving with immediate visual feedback.

Step-by-Step Solution Process

Extract coefficients from the input equations
Calculate the denominator: (b * c - a * d)
Check if denominator is zero (indicates no unique solution)
Calculate x = (b * n - d * m) / denominator
Calculate y = (a * n - c * m) / (a * d - b * c)
Round results to 4 decimal places for display