Question 123629
Let x= # of votes for winning candidate, y=# of votes for losing candidate



Because, there were 810 votes in all, this means that the sum of the votes is 810. So the first equation is 


{{{x+y=810}}}


Also, since "the winning candidate had 220 more votes than the loser", this means the second equation is {{{x=y+220}}}


So we have the system


{{{x+y=810}}}
{{{x=y+220}}}




{{{y+220+y=810}}}  Plug in {{{x=y+220}}} into the first equation. In other words, replace each {{{x}}} with {{{y+220}}}. Notice we've eliminated the {{{x}}} variables. So we now have a simple equation with one unknown.




{{{2y+220=810}}} Combine like terms on the left side



{{{2y=810-220}}}Subtract 220 from both sides



{{{2y=590}}} Combine like terms on the right side



{{{y=(590)/(2)}}} Divide both sides by 2 to isolate y




{{{y=295}}} Divide





Now that we know that {{{y=295}}}, we can plug this into {{{x=y+220}}} to find {{{x}}}




{{{x=(295)+220}}} Substitute {{{295}}} for each {{{y}}}



{{{x=515}}} Simplify



Answer:


So our answer is {{{x=515}}} and {{{y=295}}} which means that the winning candidate had 515 votes and the losing candidate had 295 votes