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
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 on
cherry trees and
rose bushes. Jose spent
on
cherry trees and
rose bushes. Find the cost of one cherry tree and the cost of one rose bush.
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:
cherry trees and
rose bushes
For Jose:
cherry trees and
rose bushes
Now, we have a system of equations
We can solve this by process of substitution, elimination or fraction.
Since the value of is the same for both equations, let’s do the process of elimination.
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 by dividing both sides by
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 by getting one equation and plugging the value of
.
Let’s use the first equation to plug in
Let’s isolate by subtracting
on both sides of the equation
Then divide by
And we get
Now, we know that cost of a rose bush is .
Caddell Prep offers online test prep, web-based math assignments, and in-person tutoring and test prep.