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.