AIM: How do we solve systems of equations using elimination by adding and subtracting? Do Now: Find the solution to the following system: Use the provided.

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Presentation transcript:

AIM: How do we solve systems of equations using elimination by adding and subtracting? Do Now: Find the solution to the following system: Use the provided coordinate plane. Is this a one solution, no solution, or infinitely many solution system?

HW Review: Regents Review 4 is due tomorrow You will have a quiz this Friday

BIG IDEAS We are looking for the solutions of these systems of equations. Solutions are expressed in the form of a coordinate – (x, y). Last week, we graphed each line and looked for the solution, today, we’re going to find the solution algebraically, using ELIMINATION.

Quick Reminder… Addition Property of Equality: -6x + 6x = 0 4y + (-4y) = 0

Solving by Elimination: We can use elimination when equations are in standard form, like this: -2x + 6y = 12 3x - 6y = 8 Elimination requires you to ELIMINATE one variable. In the two equations above, which variable makes the most sense to eliminate? Why? Same coefficients!

Steps to Solving Systems of Equations: Using Elimination 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. Solve for the variable. Substitute the value of the variable into the equation. Substitute your ordered pair into BOTH equations.

Example #1: Solving by Adding Find the solution to this system.

Example #2: Solving by Subtracting Find the solution to this system:

Groupwork Expectations: Get into your assigned groups in under 1 minute Complete all of the assigned work and return to me at the end of class If you have a question, please ask a group member first, then, if you are still stuck, ask me by raising your hand Please work as quickly and quietly as possible Return the desks to rows before we all leave

Summary: What is the most important thing to remember about solving systems of equations by elimination? When would you use elimination instead of graphing?