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Solving Systems of Equations via Elimination

Learn how to solve systems of equations using the elimination method. Understand the concept of equivalent systems and the rules that govern them. Discover real-life applications through word problems.

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Solving Systems of Equations via Elimination

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  1. Solving Systems of Equations via Elimination D. Byrd February 2011

  2. Equivalent Systems • Systems of equations are equivalent if they have the same solutions • Theorem on Equivalent Systems (p. 574) • Given a system of equations, an equivalent system results if • two equations are interchanged • an equation is multiplied/divided by a nonzero constant • one equation is added to another • Rules 2 and 3 are often combined • “Add 3 times equation (b) to equation (a)”

  3. Theorem on Equivalent Systems • Do rules of Theorem on Equivalent Systems make sense? • “An equivalent system results if… • “two equations are interchanged”: obvious! • “an equation is multiplied (or divided) by a nonzero constant”: pretty obvious • “one equation is added to another”: huh? • Demo with Geometers Sketchpad

  4. Solving Systems by Elimination • Example 1: elimination two different ways x + 3y = –1 2x – y = 5

  5. Solving Systems by Elimination • Example 2 3x + y = 6 6x + 2y = 12 • Example 3 3x + y = 6 6x + 2y = 20

  6. Characteristics of Systems of Two Linear Equations in Two Unknowns

  7. Word Problems #*(#$*@*&

  8. An Application: Boat vs. Current Speed • Motorboat at full throttle went 4 mi. upstream in 15 min. • Return trip (with same current, full throttle) took 12 min. • How fast was the current? The boat? • Use d = rt (distance = rate * time)

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