Solve systems of linear equations with interactive calculator and Visual Basic examples
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:
2x + 3y = 8
4x - y = 6
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
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
The solver uses algebraic elimination to find solutions for the system of equations.
Checks for division by zero which occurs with dependent or inconsistent equations.
Shows both VB6 and modern VB.NET approaches with proper validation.
Real-time equation solving with immediate visual feedback.