Getting only 1 radio button to be saved instead of 2 - laravel

Question

In my page I can have multiple addresses, but the user can only select one address.
The problem I'm having is that both my radio buttons are being saved instead of just one.
So if the user has 2 addresses then only one should have selected = 1 and the other address should be selected = 0, but at the moment both address = 1.
I haven't been able to only have 1 address selected and saved as such in the database. I know that I'm passing the ID of the selected radio button through, but I was hoping to have this happen.
E.G: When the user saves their first address that is then saved as their selected address (selected = 1) and any other addresses they add after that will be (selected = 0).
If they change their mind and want their second address to be the one they use then the select it and that will then become like this, address 1 (selected = 0) and address 2 will become (selected = 1).
I hope this made sense. If it didn't please let me know.
My form
#foreach($addresses as $address)
<div class="col-lg-4">
<form id="address-radio" action="{{ route('account.post.addresses.radio', $address->id) }}" method="post">
#csrf
<div class="form-check">
<input type="radio" class="form-check-input" name="address_option" id="address_{{ $address->id }}" {!! $address->selected == '1' ? 'checked' : '' !!}>
<label for="address_{{ $address->id }}" class="form-check->label">
#if(!empty($address->complex))
{{ $address->complex }} <br>
#endif
{{ $address->address }} <br>
{{ $address->suburb }} <br>
{{ $address->city }} <br>
{{ $address->province }} <br>
{{ $address->postal_code }} <br>
</label>
</div>
</form>
</div>
#endforeach
<script>
$(document).ready(function(){
$('input[type="radio"]').on('change', function(){
$(this).closest("form").submit();
})
})
</script>
and this is my function
public function postAddressesRadio(Request $request, $id)
{
$selected = Address::findOrFail($id);
$user_id = Auth::user()->id;
$not_selected = $selected->where('id', '!=', $id)
->where('user_id', $user_id)->get();
foreach($not_selected as $selected)
{
$selected->selected = "0";
}
if($request->address_option == 'on'){
$selected->selected = '1';
}
$selected->save();
return redirect()->back()->with('success', 'Address was updated');
}

Answer 1

So I've managed to do it. I'm not sure if there is a better way but this works.
In my function I did
public function postAddressesRadio(Request $request, $id)
{
$address = Address::findOrFail($id);
$user_id = Auth::user()->id;
$addresses = Address::where('user_id', $user_id)->get();
foreach($addresses as $address)
{
if($address->id == $id)
{
$address->selected = "1";
}else{
$address->selected = "0";
}
$address->save();
}