Let’s Play a Game…

Pull out a piece of paper (rip it in half) Write down a Number (any number you want) Call it x ( x = ____ ) Now Pick Another Number Call it y ( y = ____ )

What does x + y = ? What does x – y = ? Example : x = 3 y = 5 x + y = 8 x – y = -2

On your blank piece of paper, write down YOUR EQUATIONS ONLY! Switch Papers with Someone Switch Papers with Someone Else Switch Papers with One More Person (make sure you don’t have your own paper)

Example : x + y = 7 x – y = 13 2x + 0 = 20 2x = 20 x = 10 Once you know x, how do you find y? SUBSTITUTION! (You can use either equation) x + y = 7 (10) + y = y = -3 This method is called ELIMINATION

Can I solve real situations using equations? ᶱ Define your variables. ᶱ Create equations based on the information provided. ᶱ You can solve for both variables using: ᶱ Elimination ᶱ Substitution ᶱ Graphs YES!

Substitution Choose one equation and isolate a variable. Substitute the solution from step 1 into the second equation and solve for the variable in the equation. Using the value found in step 2, substitute it into the first equation and solve for the 2 nd variable. Substitute the values you found into the original equations and check your solutions

Elimination We already looked at an example of this but here are the steps…

Step 1: Put the equations in Standard Form. Step 2: Determine which variable to eliminate. Step 3: Add or subtract the equations. Step 4: Plug back in to find the other variable. Step 5: Check your solution. Standard Form: Ax + By = C Look for variables that have the same coefficient. You may need to multiply to ensure they are the same. Solve for the variable. Substitute the value of the variable into the equation. Substitute your ordered pair into BOTH equations. Elimination

Graphing Graph both equations on a coordinate plane. Find the point of intersection. Write your answer as a coordinate point. You can do this on your calculator

Mrs. Drawbaugh decided to purchase candy for her whole class as a treat. She bought Smarties and Dum-Dum lollipops as “brain food” for their next exam. Each bag of Smarties cost $7.00 (including tax). The bag of Dum-Dum lollipops cost $8.50 (including tax). She ended up spending $60.50 on her purchase of 8 items.

Smarties: $7.00 Dum-Dum lollipops: $8.50 Number of Smarties Bags Number of Dum-Dum lollipops Bags Total Cost for 8 Items ($) Determine the number of Smartie Bags and Dum- Dum lollipop Bags Mrs. Drawbaugh bought with $ $ $ $ $ $ $ $ $ $56.00

Smarties: $7.00 Dum-Dum lollipops: $ bags of candy bought total

Elimination 5 Smarties bags 3 Dum-Dum lollipop bags (Multiply by to eliminate the x-values) (Keep the equation as-is)

Substitution Substitute 5 for x in either equation to solve for y 5 Smarties bags 3 Dum-Dum lollipop bags

Graphing 5 Smarties bags 3 Dum-Dum lollipop bags You can do this on your calculator

I want to hear your ideas first and then I’ll share mine with you…

Business Expense Models

Package Comparisons

Significant Events

2010

Economics

MAXIMUM WEIGHT = BREAKING POINT

When solving a System of LINEAR equations you will have either: One Solution No Solution Infinite Solutions (intersects at one point) (Never intersects)(Intersects infinitely– Same Line)