Question 146202
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 {{{2w+t=57}}}


And the sentence "They won 9 more games than they tied" translates to the second equation {{{w=t+9}}}





Start with the given system

{{{2w+t=57}}}
{{{w=t+9}}}




{{{2(t+9)+t=57}}}  Plug in {{{w=t+9}}} into the first equation. In other words, replace each {{{w}}} with {{{t+9}}}. Notice we've eliminated the {{{w}}} variables. So we now have a simple equation with one unknown.



{{{2t+18+t=57}}} Distribute



{{{3t+18=57}}} Combine like terms on the left side



{{{3t=57-18}}}Subtract 18 from both sides



{{{3t=39}}} Combine like terms on the right side



{{{t=(39)/(3)}}} Divide both sides by 3 to isolate t




{{{t=13}}} Divide





Now that we know that {{{t=13}}}, we can plug this into {{{w=t+9}}} to find {{{w}}}




{{{w=(13)+9}}} Substitute {{{13}}} for each {{{t}}}



{{{w=22}}} Simplify



So our answer is {{{w=22}}} and {{{t=13}}} which means that the team won 22 games and tied 13 games