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Objective: Solve a system of two linear equations in two variables by elimination. Standard:

Objective: Solve a system of two linear equations in two variables by elimination. Standard: 2.8.11.H. Select and use an appropriate strategy to solve systems of equations. 3.2 Solving Systems by Elimination. I. Elimination Method

sydney-smith
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Objective: Solve a system of two linear equations in two variables by elimination. Standard:

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  1. Objective: Solve a system of two linear equations in two variables by elimination. Standard: 2.8.11.H. Select and use an appropriate strategy to solve systems of equations. • 3.2 Solving Systems by Elimination

  2. I. Elimination Method The elimination method involves multiplying and combining the equations in a system in order to eliminate a variable. 1. Arrange each equation so they are in the same form. 2. Choose to eliminate either x or y. 3. If the coefficients of the variable you chose to eliminate are different, multiply one or both equations to make the coefficients the same size but opposite sign. 4. Add the like terms of the equations 5. Use substitution to solve for the remaining variable.

  3. Independent Systems • Ex 1. Use elimination to solve the system. Check your solution. 2x + y = 8 x – y = 10

  4. Ex 2. Use elimination to solve the system. Check your solution. 2x + 5y = 15 –4x + 7y = -13

  5. Use elimination to solve the system. Check your solution. 4x – 3y = 15 8x + 2y = -10

  6. Ex 2. This table gives production costs and selling prices per frame for two sizes of picture frames. How many of each size should be made and sold if the production budget is $930 and the expected revenue is $1920? 5.5x + 7.5y = 930 12x + 15y = 1920 * Multiply by -2 -11x – 15y = -1860 12x + 15y = 1920 x= 60 small y = 80 large

  7. II. Dependent and Inconsistent Systems Ex 1. Use elimination to solve the system. Check your solution. 2x + 5y = 12 2x + 5y = 15 ** Multiply by – 1 to first equation -2x – 5y = -12 2x + 5y = 15 0 = 3 Empty Set Inconsistent Parallel Lines (both equations have a slope of -2/5)

  8. II. Dependent and Inconsistent Systems Ex 2. Use elimination to solve the system. Check your solution. -8x + 4y = -2 4x – 2y = 1 -8x + 4y = - 2 8x - 4y = 2 Multiplied by 2 0 = 0 ∞ Consistent Dependent

  9. Use elimination to solve the system. Check your solution. 1. 5x - 3y = 8 3. 4y + 30 = 10x 10x – 6y = 18 5x – 2y = 15 4. 5x + 3y = 2 2. 6x – 2y = 9 2x + 20 = 4y 6x – 2y = 7

  10. Writing Activities

  11. Homework Integrated Algebra II- Section 3.2 Level A Honors Algebra II- Section 3.2 Level B

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