3.7 Solving by Substitution

GRAPH: The Problem with Graphing

You have to make a decision about how to spend your grocery budget. Here are your options:

• You can continue shopping at your local grocery store where you will spend $100 per week on essential groceries

• You can get a membership at your local Costco where you will pay a $55 membership fee but will pay only $80 per week for groceries

Solving Systems by Substitution

While graphing can be used to show the intersection of two lines, it has its limitations. If we are looking for a precise answer, we can calculate the solution using algebra.

The substitution method allows you to calculate the solution of a system by solving one equation for a variable, then substituting that equation into the other equation of your system.

1. Review the example problem completed below.

1

Isolate one variable: Solve one equation for either variable (if necessary)

2

Substitute:

Substitute that solved equation into the other equation.

3

Solve: There should only be one variable remaining. Solve that for that variable.

4

Plug in:

To find the other variable, plug your solution into one of the original equations and solve.

5

Check it:

Check your solution by plugging into BOTH equations of the system to be sure that you get a true statement

6

Answer:

Write your answer as a point (x, y)

(4, -1)

* Paper Copy of Student activity Sheet, Pages 4 & 5:

APPLICATION: Solving by Substitution for Savings Goals

Level 1

Building an Emergency Fund

You are working two part-time jobs. Working at the local library pays $15 per hour and working as a personal trainer pays $20 per hour. Last week you made $800 and worked 45 total hours.

Simple Interest

Remember the simple interest equation I=Prt where P represents principal balance, r represents the interest rate as a decimal, and t represents time. If you need a refresher on using the simple interest formula, click here!

Malik deposits $350 into a simple interest savings account that earns 2% per year. Saraiah deposits $400 into a different simple interest savings account that earns 1% per year.

Turning a Profit

A break-even analysis is used to figure out how many units of a product need to be sold in order to pay expenses (aka breaking even) and turn a profit. This can be done by writing two equations:

1. The cost function which represents fixed costs (usually one time costs) and variables costs (costs that can change, usually based on the number of items produced)

2. The revenue function which represents money earned from selling the product

You open a business to make and sell custom bracelets. You purchase office equipment and a laptop to market and sell your product which costs $1150. The cost to manufacture one bracelet is $2.40 and you plan to sell them for $11.