Introduction to Systems of Equations Word Problems

Applying what we know about solving systems of linear equations in real life problems

Identifying & Setting Up

Poll

Before we get started, how do you feel when you hear that we are now going to be solving system of equation word problems?

• 🤩 Fantastic, bring on the challenge!

• 🙂 Maybe it will be okay.

• 😕 A bit concerned, but willing to try it.

• 😭 I don't wanna!

TODAY WE WILL BE FOCUSING ON ALGEBRAIC SOLUTIONS

• SUBSTITUTION

• ELIMINATION

Let's work through setting up and solving an example together...

Get ready to write down the important information!

Clara's Information

• Spent $120

• Roses: 6

• Daisies: 8

Miles' Information

• Spent $116

• Roses: 10

• Daisies: 4

Get ready for some questions!

in 3, 2, 1...

Fill in the Blank

The very first things you should write for this problem is are

Multiple Choice

Your let statements should be...

• Let x = $ of a rose bush

  y = $ of a daisy pot

• Let x = # of rose bushes

  y = # of daisy pots

• Let x = # of plants Clara buys

  y = # of plants Miles buys

Remember, let statements...

• Define the unknown variables

• Are important for organizing your work

• Should always be the first step in word problems

Fill in the Blank

What equation could we write for Clara's plant purchase?

Fill in the Blank

What equation could we write for Miles' plant purchase?

Now that we have our equations written

We need to decide what is the best method to use for solving!

Multiple Choice

What is the best method for solving this system of equations?

• Substitution

• Elimination

Multiple Select

What are the possible ways to successfully do the elimination method for this problem?

(there are more than one correct answer)

• Eliminate x by multiplying the top equation by 10 and the bottom equation by 6

• Eliminate x by multiplying the top equation by -10 and the bottom equation by 6

• Eliminate x by multiplying the top equation by 10 and the bottom equation by -6

• Eliminate y by multiplying the bottom equation by 2

• Eliminate y by multiplying the bottom equation by -2

Multiple Choice

What is the resulting system of equation if you eliminate y by multiplying the bottom equation by -2?

• 6x + 8y = 120

  20x - 8y = 232

• 6x + 8y = 120

  20x + 8y = 232

• 6x + 8y = 120

  -20x - 8y = -232

Fill in the Blank

What is the resulting equation when you combine these equations at this stage?

Fill in the Blank

What is your final answer for x when you finish solving?

Multiple Choice

Which equation must you use to find the value of y next?

• The original top equation

• The original bottom equation

• It doesn't matter, either original equation will work

Fill in the Blank

Solve for y, what is your answer?

How do you represent the final answer?

You should say:

Each rose bush costs $8 and each pot of daisies costs $9.

Congratulations

You have completed this lesson!