Example:

Here the March Hare and the Mad Hatter will help find a solution for two equations using the elimination method using a word problem.

Our problem starts as stated.

A caterer is planning a party for 64 people.  the customer has $150 to spend.  A $39 pan of pasta feeds 14 people and a $12 sandwich tray feeds 6 people.  How many pans of pasta and how many sandwich trays should the caterer make?

Now we must create the two equations.

14p+6s=64
39p+12s=150
14p equals how many people the pasta pan can feed.
6s is how many people the sandwich tray can feed.
64 is how many people will be at the party.
39p is the cost of the pasta pan.
12s is the cost of the sandwich tray.
150 is how much money the caterer can spend.

Using the elimination method we will solve first for p.  And in order to do this one must multiply the first equation by -2.

-2(14p+6s=64)
the equation now becomes 
-28p-12s=-128
39p+12s=150
add the two together to form one equation
11p=22
divide both sides by 11
p=2

Now substitute the 2 into either of the two equations and solve for s.

14p+6s=64
14(2)+6s=64
28+6s=64
subtract 28 from both sides
6s=36
divide both sides by 6
s=6