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Algebra I: Section 6-3: Solving Systems using Elimination

Learn how to solve systems of equations using the substitution and elimination methods. Practice solving various systems and understand the concept of opposites in elimination. Find the fares for rush hour and regular hours on the Metro train.

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Algebra I: Section 6-3: Solving Systems using Elimination

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  1. ALGEBRA I @ SECTION 6-3 : SOLVING SYSTEMS USING ELIMINATION

  2. Solve using substitution. 4x + y = 8 2x - y = -2 ANSWER : (1, 4) 2) Now, solve the same system of equations using elimination. The process, elimination, is also known by cancellation and linear combination.

  3. When you use the elimination method, you are looking to make opposites. What happens when you add opposites?

  4. Solve using elimination. 4x – 2y = -1 -4x + 4y = -2 2x – 3y = 16 3x + 6y = 3 ANSWER : (-1, -3/2) ANSWER : (5, -2) 3x – 2y = 21 3x + 4y = 3 2x – 5y = 1 8x – 2y = 22 ANSWER : (5, -3) ANSWER : (3, 1)

  5. 6x – 5y = 28 4x + 9y = -6 3x + 5y = 1 6x + 10y = 2 ANSWER : (3, -2) ANSWER : infinitely many 2x + 5y = 3 3x – 2y = -5 -4x + 3y = 5 8x – 6y = -9 ANSWER : (-1, 1) ANSWER : no solutions

  6. 11) Aaron and Jacob both took the Metro train to work. In November, Aaron took the train 15 times during rush hour and 29 times during regular hours for $64.80. Jacob took the train 30 times during rush hour and 14 times during regular hours for $76.80. Find the fares for rush hour and for regular hours. ANSWERS : rush hour - $2, regular hours - $1.20

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