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6.3 – Solving Systems of Linear Equations by Elimination.

Explore the Elimination Method for solving systems of linear equations. Learn how to eliminate variables to find solutions efficiently. Practice with examples and sentence frames to enhance understanding.

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6.3 – Solving Systems of Linear Equations by Elimination.

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  1. Definitions of the Day (DODs) 6.3 – Solving Systems of Linear Equations by Elimination. Review of Ch 6 Systems of Equations So Far… 6.1 Graphing 6.2 Substitution Method 6.3 Elimination Method

  2. Definition: EliminationMethod –Eliminate one of the variables by adding (or subtracting) the equations of the system.   Let us Explore… x y 10 + = Top Equation + x ( - y = ) + 36 Bottom Equation 2x = 46 Y has been ELIMINATED x 23 , y =-13 = Solve for x, Substitute for y

  3. Steps to the Elimination Method!! • Pick One Variable to Eliminate! (Either x or y.) 2.Eliminate the Variable by adding or subtracting the equations together. 3. Substitute & Solve for the last Variable.

  4. Example #1 5x - 6y = -32 3x + 6y = 48

  5. Example #2 X+Y=6 X+3Y=10

  6. WARNING! • WE MAY NEED TO MANIPULATE ONE OF THE EQUATIONS BEFORE SOLVING FOR A VARIABLE!

  7. Example #3(One Solution) 3x + 4y = -10 5x - 2y = 18

  8. Example #4(No Solution) 6x - 9y = 9 2x - 3y = 6

  9. Example #5(Infinitely Many Solutions) x + 4y = 1 3x + 12y = 3

  10. Your Turn!! Solve by ELIMINATION 1. X+ y = 12 2. 4x - 2y = 6 x - y = 2 -2x + y = -3

  11. Sentence Frames • The Goal of Solving a System of Equations by Elimination is __________________________________________________________________________________________________ • The Three methods for solving a System of Equations are 1. _______________ 2. _______________ 3. _______________

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