SOLUTION: My question is how to substitute x+y to 4x+2y. the problem is: There are 25 heads and 100 legs,x chicken(2 legs) and y pigs(4 legs). The answer is 25 pigs but I need equations to

Algebra ->  Linear-equations -> SOLUTION: My question is how to substitute x+y to 4x+2y. the problem is: There are 25 heads and 100 legs,x chicken(2 legs) and y pigs(4 legs). The answer is 25 pigs but I need equations to       Log On


   

Question 335897: My question is how to substitute x+y to 4x+2y. the problem is: There are 25 heads and 100 legs,x chicken(2 legs) and y pigs(4 legs). The answer is 25 pigs but I need equations to get to 1x=25 here is what I have so far
system%28x%2By=25%2C+4x%2B2y=100%29
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

It is obvious that they all have to be pigs with no chickens,
since 100=4*25, there are 4 times as many legs as there are heads,
and of course there are 25 pigs and no chickens.  So this is a strange
problem.  I hope the problem didn't state that there had to be some 
chickens, since there aren't any.  But anyway, we'll go through what 
was giving you trouble.

system%28x%2By=25%2C+4x%2B2y=100%29

Solve the first equation for either letter.  I will
arbitrarily choose to solve the first equation for y

x%2By=25
y=25-x

Next substitute %2825-x%29 for y in the second equation:

4x%2B2%2825-x%29=100
4x%2B50-2x=100
2x%2B50=100
2x=50
x=25

So since

y=25-x
y=25-25
y=0

So there are 25 pigs and no chickens.

Edwin