Download Section 6.2 Systems of Linear Equations in Three Variables

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

page
1
page
2
page
3
Document related concepts
no text concepts found
Transcript 
Section 6.2 Systems of Linear Equations in Three Variables
Equation: Ax + By + Cz = D
Solution: (x, y, z) an ordered triple ­ which represents a plane
• The z­axis is perpendicular to the the xy­plane
• Then we have a 3­Dimensional or xyz­coordinate system. Visualize the corner of a room: xy­plane is the floor
yz­plane is one wall
xz­plane is the other wall
Some possible representations of systems of linear equations in three variables:
We can still use the methods of substitution and elimination, taking two equations at a time and eliminating the same variable each time.
Example: Solve the System:
Example 2) If the ages of three girls, Xenia, Yolanda, and Zsa Zsa are added, the result is 30. The sum of Xenia's and Yolanda's ages is Zsa Zsa's age, while Xenia's age subtracted from Yolanda's is half of Zsa Zsa's age a year ago. How old are the three girls?
Another Application: Curve Fitting
Goal: Find an equation whose graph passes through or "fits" all of the points.
EXAMPLE:
Related documents