Respuesta :
Answer:
13 points
Step-by-step explanation:
Equation for "There are 50 athletes signed up for a neighborhood basketball competition. Players can select to play in the 6-player games ("3 on 3") or the 2-player games ("1 on 1").
Equation for "If the neighborhood holds 13 total games and all 50 athletes participate"
How many 6 player games?
How many 2 player games?
The answer to this question is:
7 two-player games are played
6 six-player games are played
What are system of equations?
A collection of two or more equations with the same set of unknowns is referred to as a system of equations.
Systems of linear equations in two variables can be solved in one of three ways:
- by graphing;
- by the substitution approach;
- or by the elimination method.
Solution:
Given:
Total games = 13
Total number of athletes participated = 50
Find:
6-player games played = ?
2-player games played = ?
Step-1:
let x denote the total 2-player games played &
y denote the total 6-player games played.
Hence the equation for the total number of games played is:
x + y = 13 ..............eq(1)
Now, the equation for the total number of games played by the athletes is:
2x + 6y = 50............eq(2)
Further eq(2) can be reduced as-
2(x + 3y) = 50
x + 3y = 50/2
x + 3y = 25.........eq(2)
Step-2:
Solving eq(1) and eq(2) by using elimination method as follows:
x + y = 13
x + 3y = 25
Step-3:
In the elimination method positive signs changes to negative and x gets eliminated so we get the y value as:
-2y = -12
y = 6
Substituting y value in eq(1): x+ y = 13
x + 6 = 13
x = 13 - 6
x = 7
Hence we found out that total 7 two-player games and 6 six-player games were played.
Learn more about "System of equations" here:
brainly.com/question/13729904
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