I don't understand an answer

Question

Nous regrettons que vous ne ________ pas participer. We regret you don't want to participate.(HINT: Conjugate "vouloir" in the Subjonctif présent)I don't understand why the answer is vouliez and not veuillez.

Maarten Kamp · Accepted Answer

Anne, 
 ‘ vouliez ‘ is the present subjunctive conjugation of vouloir for ‘ vous ‘.
 ‘ Veuillez’ is an option as an imperative form, not indicated here.
The stem for the ‘ nous ‘ and ‘ vous ‘ forms of vouloir is not the same as the stem for the singular verb forms, or the 3rd person plural form, in either the present tense or the present subjunctive.  
The subjunctive forms for nous and vous are the ‘ same words ‘ as for the imparfait forms.
Vouloir also has irregular changes in the imperative. 
As well as the lesson here, this is covered in the below links :
 https://www.lawlessfrench.com/grammar/subjunctive-irregular-conjugations/
https://www.lawlessfrench.com/verb-conjugations/vouloir/