Solving Systems of Linear Equations by
Eliminating!
Just Follow The Directions Below in Green and the Example in Brown.
Step1: Write down the two given equations.
Example 1: This example is a word problem. You will learn how to set up equations using elimination, also called linear combination.
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?
Equation 1
should be 14p + 6s = 64
..... this represents the people at the
party where pans of pasta are denoted as "p", and sandwich trays
are denoted as "s" totaling to 64 people.
Equation 2
should be 39p + 12s = 150
..... this represents how much money will be spent on food. 39 shows the price
of a pan of pasta,
12 shows the price of a sandwich tray, and the customer has $150 dollars to
spend, total.
Step 2: Multiply one or both of the equations by a constant to make both equations have a similar value and shared variable that differ in sign so that they cancel one another out, thus giving you the value of one of the variables.
Equation 1: 14p + 6s = 64
....... times -2 = -28p
- 12s = -128
Equation 2: 39p + 12s = 150 ............... =
39p
+ 12s
= 150
11p = 22
P = 2
Step 3: Once you have the value of the first variable, substitute it into the first equations to obtain the value of the second variable.
Equation 1: 14p + 6s = 64
14(2) + 6s = 64
28 + 6s = 64
- 28 -28
6s = 36
S = 6
Step 4: Write down your solution.
The caterer should make 2 pans of pasta and 6
sandwich trays for the party.