Login WordPress website using wp-rest api

I am using WordPress 4.8 and i am new to rest api . I have 2 websites , one is www.example.com and second is www.example.com/site2. That is second website is installed inside the first .

In example.com i have many users. In site 2 , i have a custom page & in that page i create a custom forms for login . The form is checking the details based on first website users . That is some one enter the login details of first website then they can able to login .
Please check my form

<form>
<input type="text" name="user_name" class="user_name" required>
<input type="password" name="user_password" class="user_password" required>
<input tuype="submit" name="submit" class="submit">
</form>

<script>

     $(".submit").on("click",function(){
           var username = $(".user_name").val();
           var password = $(".user_password").val();
            });

</script>

Please help to complete this form. Should I need to use curl ? How can I check the login details with the help of rest api