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Danger · Answer 1 · 2023-11-29T10:19:22+0000

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

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

For the blue jays: They won 7 matches, 2 draws and 1 loss for a total of 44 points. So the equation would be

Finally, for the hawks, they had 4 wins, 4 draws and 2 losses for a total of 28 points. So we have the equation

we want to solve this equations to find the value of x.

We will start by taking the first equation

we will take this equation and subtract it from the second one. So we get

$\begin{gathered} 7x+2y+1z\text{ - \lparen6x+3y+1z\rparen=44-40} \\ =\text{ 7x -6x +2y-3y+1z-1z=4} \\ =x\text{ -y=4} \end{gathered}$

that means, we have the new equation

$x\text{ -y=4}$

Now. We will take the first equation, multiply it by 2 and subtract it from the third equation. That is

$\begin{gathered} 4x+4y+2z\text{ - 2\lparen6x+3y+1z\rparen=28 -2}\cdot40 \\ =4x\text{ - 12x + 4y - 6y +2z - 2z =}28\text{ - 80 } \\ =\text{ -8x-2y= -52} \end{gathered}$

if we divide both sides by -2 we get the equation

Now, let us add this two new equations that we got. That would be

$\begin{gathered} x\text{ -y + 4x+y =}4+26 \\ =\text{ x+4x +y -y=30} \\ =\text{ 5x=30} \end{gathered}$

then, if divide both sides by 5, we get

$\begin{gathered} 5x=30 \\ x=(30)/(5)=6 \end{gathered}$

so the number of points awarded for a win is 6

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