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6.3 Solving Systems Using Elimination:

Solution of a System of Linear Equations: Any ordered pair that makes all the equations in a system true. 6.3 Solving Systems Using Elimination:. Substitution Method: Isolate a variable in an equation and substitute into the other equation.

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6.3 Solving Systems Using Elimination:

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  1. Solution of a System of Linear Equations: Any ordered pair that makes all the equations in a system true. 6.3 Solving Systems Using Elimination: Substitution Method: Isolate a variable in an equation and substitute into the other equation. Elimination Method: Eliminating one variable at a time to find the solution to the system of equations.

  2. Remember:

  3. GOAL:

  4. USING ELIMINATION: To solve a system by the elimination method we must: 1) Pick one of the variables to eliminate 2) Eliminate the variable chosen by converting the same variable in the other equation its opposite(i.e. 3x and -3x) 3) Add the two new equations and find the value of the variable that is left.

  5. USING ELIMINATION: Continue 4) Substitute back into original equation to obtain the value of the second variable. 5) Check, substitute the values found into the equations to see if the values make the equations TRUE.

  6. NOTE: In order to eliminate a number or a variable we add its opposite. Ex:to eliminate 5, we add -5 x, we add –x 3y, we add -3y -3.5x, we add 3.5x TRY IT: What do you add to eliminate: a) 30xy b) -1/2x c) 15y SOLUTION: a) -30xy b) +1/2x c) -15y

  7. USING ELIMINATION: we carry this procedure of elimination to solve system of equations. Ex:What is the solution of the system? Use elimination.

  8. SOLUTION: 1) Pick one of the variable to eliminate. Looking at the system, y will be easy to eliminate. 2) Eliminate the variable chosen by converting the same variable in the other equation its opposite. In our system this is already done since +5y and -5y are opposites.

  9. SOLUTION: 3) Add the two new equations and find the value of the variable that is left. Add them: +

  10. SOLUTION: 4) Substitute back into original equation to obtain the value of the second variable. OR Solution: (1, 3)

  11. SOLUTION: 5) Check: substitute the variables to see if the equations are TRUE. and

  12. YOU TRY IT:What is the solution of the system? Use Elimination.

  13. SOLUTION: 1) Pick one of the variable to eliminate. Looking at the system, y will be easy to eliminate. 2) Eliminate the variable chosen by converting the same variable in the other equation its opposite. In our system this is already done since -y and +y are opposites.

  14. SOLUTION: 3) Add the two new equations and find the value of the variable that is left. Add them: +

  15. SOLUTION: 4) Substitute back into original equation to obtain the value of the second variable. OR Solution: (2, 3)

  16. SOLUTION: 5) Check: substitute the variables to see if the equations are TRUE. and

  17. VIDEOS: Elimination https://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/fast-systems-of-equations/v/solving-systems-of-equations-by-elimination

  18. CLASSWORK:Page 378-380 Problems: As many as needed to master the concept.

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