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Let’s Play a Game…

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.

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Let’s Play a Game…

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  1. Let’s Play a Game…

  2. 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 = ____ )

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

  4. 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) Switch Papers with Someone Else

  5. What does x = ? What does y = ? Be able to explain your strategy!

  6. SUBSTITUTION! (You can use either equation) Example: x + y = 7 x – y = 13 2x + 0 = 20 2x = 20 x = 10 Once you know x, how do you find y? x + y = 7 (10) + y = 7 -10 -10 y = -3 This method is called ELIMINATION Do your answers make sense? Double check using the original equations.

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

  8. 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 2nd variable. Substitute the values you found into the original equations and check your solutions

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

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

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

  12. 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.

  13. Smarties: $7.00 Dum-Dum lollipops: $8.50 Determine the number of Smartie Bags and Dum-Dum lollipop Bags Mrs. Drawbaugh bought with $60.50.

  14. Smarties: $7.00 Dum-Dum lollipops: $8.50 8 bags of candy bought total

  15. Elimination (Multiply by -7.00 to eliminate the x-values) (Keep the equation as-is) 5 Smarties bags 3 Dum-Dum lollipop bags

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

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

  18. When are you ever going to need this? I want to hear your ideas first and then I’ll share mine with you…

  19. Business Expense Models

  20. Package Comparisons

  21. Significant Events

  22. 2010

  23. Economics

  24. MAXIMUM WEIGHT = BREAKING POINT

  25. Will the Asteroid hit the Earth?

  26. 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)

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