Respuesta :
Answer:
They won 17 games and drew 4 games
Step-by-step explanation:
The given parameters are;
The number of points the major league soccer team finished with = 55 points
The number of games the soccer team played = 28 games
The number of losses the soccer team had = 7 losses
The number of points awarded for each win = 3 points
The number of points awarded for each tie = 1 points
The number of points awarded for each loss = 0 points
Let x represent the number of wins, y represent the number of draws, and let z represent the number losses
Therefore;
z = 7
x + y + z = 28
3·x + y + 7×0 = 55
Therefore, we have the following system of equations;
x + y = 21...(1)
3·x + y = 55...(2)
Which gives;
[tex]\begin{bmatrix}1 & 1\\ 3 & 1\end{bmatrix} \begin{bmatrix}x \\ y\end{bmatrix} = \begin{bmatrix}21 \\ 55\end{bmatrix}[/tex]
The inverse of the matrix is given as follows;
[tex]\dfrac{1}{1 - 3} \times \begin{bmatrix}1 & -3\\ -1 & 1\end{bmatrix} = \begin{bmatrix}-0.5 & 0.5\\ 1.5 & -0.5\end{bmatrix}[/tex]
Therefore;
[tex]\begin{bmatrix}x \\ y\end{bmatrix} = \begin{bmatrix}-0.5 & 0.5\\ 1.5 & -0.5\end{bmatrix} \times \begin{bmatrix}21 \\ 55\end{bmatrix} = \begin{bmatrix}17 \\ 4\end{bmatrix}[/tex]
x = 17, y = 4
