I have a C# Form, where you have Form1 shown at the start, and when you press Go you are taken to Form2. Form1
Try this:
Hide();
Form2 form2 = new Form2();
form2.Closed += (s, args) => this.Close();
form2.Show();
This will close Form1 when you close Form2. If the user presses X or ALT+F4 or RightClick -> Close on Form2 The Form2 and the hidden Form1 will close.
Use the FormClosed event on Form2 to exit the application.
private void Form2_FormClosed(object sender, FormClosedEventArgs e)
{
Application.Exit();
}