Unit 2: Systems of Equations
Substitution
Unit 2
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Unit 2: Systems of Equations
Substitution
You are walking through the halls when you decide to get a water from the
vending machine. Even though you have 5 dollars in one dollar bills, the vending
machine is broken and will only accept coins.
YOU NEED TO MAKE CHANGE!
You see a friend and ask if you can make change for a dollar. Since you know a
dollar and four quarters are the same amount of money, your friend gives you four
quarters to replace one of your dollars.
=
Even though you still have the same amount of money as you did before, you
now have the quarters you need to get your water from the vending machine.
Your money after
making change
Your money before
making change
=
TOTAL:
5 dollars
=
5 dollars
The process of removing one value and replacing it with an equal value of something
else is called SUBSTITUTION. Substitution is one of the methods we use to solve a
system of equations.
So how will we use this?
Unit 2: Systems of Equations
Substitution
You are going to a birthday party and are in charge of buying cookies. You really want
Oreo cookies, but they cost two times as much as the Market Basket brand cookies.
You don’t have much money, so you buy three boxes of Oreos and one box of Market
Basket cookies. All together, the cookies cost 14 dollars. How much money does a
box of Oreos cost?
The first thing we want to do is define our variables. This means we need to assign a
letter for each of the values that we don’t know.
X = Market Basket cookies
Y = Oreos
Once we have defined our variables, we want to write our equations. The first
equation can be written using the phrase “You really want Oreo cookies, but they cost
two times as much as the Market Basket brand cookies”.
=
Y
=
Algebraically, we would write this as
2x
y = 2x
We can write our second equation using the statement “you buy three boxes of Oreos
and one box of Market Basket cookies. All together, the cookies cost 14 dollars.”
+
X
+
3Y
=
$14
=
14
Since Market Basket cookies are represented by x and Oreos are represented by y, we
can write this equation as
x + 3y = 14
We now have our system of equations:
y = 2x
x + 3y = 14
Unit 2: Systems of Equations
Substitution
You might not feel comfortable solving a system of equations, but you can probably
figure it out formally. Let’s compare:
=
= $14
+
Since two boxes of Market Basket cookies is the same cost as one box
of Oreos, we can replace each box of oreos with two boxes of Market
Basket cookies.
+
= $14
+
= $14
If seven boxes of Market Basket cookies are 14 dollars total, you
can divide by seven to find out how much one box of Market
Basket cookies costs.
= $2
Now that we know the value of one variable, we can substitute again to find
the second variable
=
= $2 $2
= $4
Unit 2: Systems of Equations
Substitution
Unit 2: Systems of Equations
Substitution
Unit 2: Systems of Equations
Substitution
Unit 2: Systems of Equations
Substitution