SOLUTION: Hockey teams receive 2 points when they win and 1 point when they tie. One season, a team won a championship with 57 points. They won 9 more games than they tied. How many wins

Question 146202: Hockey teams receive 2 points when they win and 1 point when they tie. One season, a team won a championship with 57 points. They won 9 more games than they tied. How many wins and how many ties did the team have?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let w=# of wins, and t=# of ties

The sentences "Hockey teams receive 2 points when they win and 1 point when they tie. One season, a team won a championship with 57 point" translate to the first equation

And the sentence "They won 9 more games than they tied" translates to the second equation

Start with the given system

Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute

Combine like terms on the left side

Subtract 18 from both sides

Combine like terms on the right side

Divide both sides by 3 to isolate t

Divide

Now that we know that , we can plug this into to find

Substitute for each

Simplify

So our answer is and which means that the team won 22 games and tied 13 games

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