Combine multiple forms $_GET values into query string - php

Question

So, i have 2 forms to filter products, one with checkboxes and the other with select options.
When i check one checkbox the form is submited and the query string is updated with it's value, when i check another checkbox the same happens, but when i select a option, the current query string resets and add only that option value instead of adding it after or before the current query.
What i want is to unite both $_GET indexes in the query string, independent of the order of submit. How can i do this? I'll be grateful if someone knows.
$marca_get = isset($_GET['marca']) && is_array($_GET['marca'])
? $_GET['marca'] : [];
if ( isset($_GET['ordem']) ) {
if ( $_GET['ordem'] == 'vendas' ) {
$orderby = 'vendas';
}
if ( $_GET['ordem'] == 'avaliacoes' ) {
$orderby = 'avaliacoes';
}
}
<form method="get">
<input type="checkbox" id="amd" class="checkbox-filtro" name="marca[]"
value="amd">
<label for="amd">AMD</label>
<input type="checkbox" id="intel" class="checkbox-filtro" name="marca[]"
value="intel">
<label for="intel">Intel</label>
</form>
<form method="get">
<select id="ordem" name="ordem">
<option value="vendas">Mais vendidos</option>
<option value="avaliacoes">Melhor avaliados</option>
</select>
</form>
$('#ordem, .checkbox-filtro').on('change', function() {
this.form.submit();
});

Answer 1

Quotes from Mozilla Developer Network:
The HTML <form> element represents a document section that
contains interactive controls for submitting information to a web
server.
When a form uses the get method, the fields are put into the URL Query String:
get: Corresponds to the HTTP GET method; form data are appended to the action attribute URI with a '?' as separator, and the resulting URI is sent to the server.
Your page has two forms, which is OK if they are unrelated. For example a page with a search form in the header, and a comment form at the bottom, would have separate forms because they do different things. The search form is also likely to have a different action URL than the comment form.
Option 1
The easiest way to get two forms to share state, is to just use one form instead of two.
If you want two forms to be united, and they also share the same action URL, this indicates that they are basically the same form.
The form element groups the fields that belong to a particular action.
The default style of a form element means users cannot see the form's boundary, and a form element can contain other 'non-form' content, just like a form on paper would.
Option 2
Copy the other form's fields, but make them hidden.
<input type="hidden" name="ordem" value="<?php echo $_GET['ordem']; ?>">
Suppose your visual design has exposed a form's boundary (CSS border or background). It may not be visually desirable to contain a significant amount of content.
This is slightly more maintenance. It may be worth redesigning the HTML/CSS so the form element is not styled directly.