1 / 8

80 likes | 230 Vues

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

Télécharger la présentation
## Solving Systems of Equations via Elimination

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**Solving Systems of Equations via Elimination**D. Byrd February 2011**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)”**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**Solving Systems by Elimination**• Example 1: elimination two different ways x + 3y = –1 2x – y = 5**Solving Systems by Elimination**• Example 2 3x + y = 6 6x + 2y = 12 • Example 3 3x + y = 6 6x + 2y = 20**Characteristics of Systems of Two Linear Equations in Two**Unknowns**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)

More Related