Answer :
Let x be the amount of points awarded for a win, y the amount of points awarded for a draw and z the amount of points awarded for a loss.
If a teams wins 6 matches, then the number of points awarded for 6 win games would be
[tex]6x[/tex]so, we will write an equation for each of the teams.
For the cardinals, they won 6 matches, 3 draws and 1 loss for a total of 40 points. So the equation would be
[tex]6x+3y+1z=40[/tex]For the blue jays: They won 7 matches, 2 draws and 1 loss for a total of 44 points. So the equation would be
[tex]7x+2y+1z=44[/tex]Finally, for the hawks, they had 4 wins, 4 draws and 2 losses for a total of 28 points. So we have the equation
[tex]4x+4y+2z=28[/tex]we want to solve this equations to find the value of x.
We will start by taking the first equation
[tex]6x+3y+1z=40[/tex]we will take this equation and subtract it from the second one. So we get
[tex]\begin{gathered} 7x+2y+1z\text{ - \lparen6x+3y+1z\rparen=44-40} \\ =\text{ 7x -6x +2y-3y+1z-1z=4} \\ =x\text{ -y=4} \end{gathered}[/tex]that means, we have the new equation
[tex]x\text{ -y=4}[/tex]Now. We will take the first equation, multiply it by 2 and subtract it from the third equation. That is
[tex]\begin{gathered} 4x+4y+2z\text{ - 2\lparen6x+3y+1z\rparen=28 -2}\cdot40 \\ =4x\text{ - 12x + 4y - 6y +2z - 2z =}28\text{ - 80 } \\ =\text{ -8x-2y= -52} \end{gathered}[/tex]if we divide both sides by -2 we get the equation
[tex]4x+y=26[/tex]Now, let us add this two new equations that we got. That would be
[tex]\begin{gathered} x\text{ -y + 4x+y =}4+26 \\ =\text{ x+4x +y -y=30} \\ =\text{ 5x=30} \end{gathered}[/tex]then, if divide both sides by 5, we get
[tex]\begin{gathered} 5x=30 \\ x=\frac{30}{5}=6 \end{gathered}[/tex]so the number of points awarded for a win is 6
