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Solving Word Problems
To solve a word problem using a system of equations, it is important to;
– Identify what we don’t know
– Declare variables
– Use sentences to create equations
An example on how to do this:
Mary and Jose each bought plants from the same store. Mary spent $188 on 7 cherry trees and 11 rose bushes. Jose spent $236 on 13 cherry trees and 11 rose bushes. Find the cost of one cherry tree and the cost of one rose bush.
Cost of a cherry tree:
Cost of a rose bush:
7 cherry trees and 11 rose bushes = $188
The y-values cancel each other out, so now you are left with only x-values and real numbers.
Then, you plug in your x-value into an original equation in order to find the y-value.
Cost of a cherry tree: $8
Cost of a rose bush: $12
Examples of Word Problems – System Of Equations
Example 1
Three coffees and a cupcake cost a total of 
Let’s solve this by following steps.
1. What we don’t know:
Cost of a single coffee
Cost of single cupcake
2. Declare variables:
Cost of a single coffee=
Cost of single cupcake=
3. Use sentences to create equations.
Three coffees and a cupcake cost a total of
Two coffees and four cupcake cost a total of
Now, we have a system of equations:
Let’s solve for one of the variables in one of the equations and then use that to substitute into the other.
Now, solve for the value of 
Let’s solve the value of 
Distribute 
Combine like terms
Now, let’s isolate the 
Then divide both sides by 
And we’ll have
Then, let’s plug the value of
Cost of a single coffee=
Cost of single cupcake=
Example 2
The senior class at High School A rented and filled 
Let’s solve this by following steps.
1. What we don’t know:
Students in each van
Students in each bus
2. Declare variables:
Students in each van=
Students in each bus=
3. Use sentences to create equations.
High School A rented and filled 8 vans and 8 buses with 240 students.
High School B rented and filled 4 vans and 1 bus with 54 students.
Now, we have a system of equations:
Let’s solve for one of the variables in one of the equations and then use that to substitute into the other.
Now, solve for the value of 
Let’s solve the value of 
Distribute
Combine like terms
Now, let’s isolate the 
Then divide both sides by 
And we’ll have
Then, let’s plug the value of
Students in each van=
Students in each bus=
Video-Lesson Transcript
To solve a word problem using system of equations, it is important to:
1. Identify what we don’t know
2. Declare variables.
3. Use sentences to create equations.
Let’s have an example:
Mary and Jose each bought plants from the same store. Mary spent 
Let’s solve this by following steps above.
1. What we don’t know:
cost of a cherry tree
cost of a rose bush
2. Declare variables:
cost of a cherry tree :
cost of a rose bush :
3. Use sentences to create equations.
For Mary:
For Jose:
Now, we have a system of equations
We can solve this by process of substitution, elimination or fraction.
Since the value of
First, let’s multiply the first equation by
Here we’ll have a negated equation
Let’s do the process of elimination now
We’ll have
Then, let’s isolate
Now, we have
Remember, our declared variable?
cost of a cherry tree :
Since
Now we can say that
cost of a cherry tree :
Now, let’s solve for the value of
Let’s use the first equation to plug in
Let’s isolate 
Then divide by
And we get
Now, we know that cost of a rose bush is 
