Question

At a park, there are 38 people playing tennis some or playing doubles and some are playing singles there are 13 matches in progress, A doubles match requires 4 players and a singles match requires 2 players.
a. write a system of two equations that represents the number of singles and doubles matches going on.

b. how many matches of each kind are in progress

Answer 1

X = number of singles matches
y = number of doubles mnathes

so we have the equation x + y = 13.......(1)

also 

2x + 4y  = 38 ...........(2)

(1) and (2) are the required equations

b)  Find how many maches are in progress by solivng the above equations:-

x + y  =  13   multiply this by -2:-
-2x - 2y = -26
2x + 4y = 38   Adding to removes the  terms in x:-

2y = 12

y = 6  

so x = 13-6 = 7

So the answer is  6 double matches and 7 singles are in progress.