Download presentation

Presentation is loading. Please wait.

1
**5.2 Systems of Linear Equations in Three Variables**

2
**Example: Solve x + 2y + z = 4 4y – 3z = 1 5z = 5**

This system is in Triangular Form (its equations follow a stair-step pattern). Example: Solve x + 2y + z = y – 3z = z = 5 Solve for one of the variables, somewhere 5z = z = 1 Now substitute into the other equations x + 2y = y – 3(1) = 1

3
**Solve the 2nd equation for y**

4y = 4 y = 1 Now, solve the 1st equation for x x + 2(1) + 1 = 4 x = x = 1 (1, 1, 1)

4
**Example: Solve: x + y + z = 0 2x + 2y – 3z = 5 x – 4y – 3z = –11**

This system is not in triangular form. Use elimination to get it in triangular form, or linear combinations to produce a system of 2 equations in 2 variables... Example: Solve: x + y + z = x + 2y – 3z = x – 4y – 3z = –11 We will use linear combinations in the 1st and 2nd equations to eliminate the z terms : 3 (x + y + z = 0) x + 3y + 3z = 0 2x + 2y – 3z = x + 2y – 3z = x + 5y = 5

5
**We will do the same for the 2nd and 3rd equations:**

2x + 2y – 3z = x + 2y – 3z = 5 –1(x – 4y – 3z = –11) –x + 4y + 3z = 11 x + 6y = 16 We now have now produced a system of 2 equations in 2 variables… 5x + 5y = 5 x + 6y = 16

6
x + 6y = x + 5y = 5 –5x – 30y = – x y = 5 –25y = –75 y = 3

7
Now, find x: x + 6(3) = x = 16 x = –2 Finally, go back to one of the original equations to find z: x + y + z = 0 – z = 0 1 + z = 0 z = –1 (–2, 3, –1)

Similar presentations

OK

A f r i d i i m r a n 94@yahoo.com S O L V IN G S Y ST E M S O F E Q U A T I O N S A f r i d i i m r a n 94@yahoo.com.

A f r i d i i m r a n 94@yahoo.com S O L V IN G S Y ST E M S O F E Q U A T I O N S A f r i d i i m r a n 94@yahoo.com.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on indian air force free download Ppt on model view controller mvc Ppt on yoga and aerobics Ppt on forward rate agreement Ppt online shopping project in vb Ppt on phase sequence checker for three phase supply Ppt on leadership styles with examples Ppt on mars one hoax Ppt on aircraft landing gear system ppt Ppt on earth hour video