Download presentation

Presentation is loading. Please wait.

Published byJake Jackson Modified over 4 years ago

1
Solving Systems of Linear Equations in Three Variables

2
A solution of a system of equations in three variables in an ordered triple (x,y,z) that makes all three equation true.

3
Solving systems using elimination x + y + z = 6 1 2x – y +3z = 9 2 -x + 2y + 2z = 9 3

4
Add 1 and 3 together. This will cancel out an x- term

5
Next, multiply 1 by -2, then add 1 and 2 together to eliminate the x- term.

6
Use a and 5 together to solve for z

7
By using 4 and 6 together we can solve for y. 3y + 3z =15 4 3y +3(3) = 15 3y + 9 = 15 3y = 15- 9 3y = 6 Y = 2 7

8
Substitute 6 and 7 into 1 to solve for x. X + y + z = 6 X + (2) + (3) =6 X + 5 = 6 X = 1

9
( 1, 2, 3 ) Write the solution as an ordered triple.

10
Creamers Rule For A 3 x 3 System

11
Let A be the coefficient matrix of this linear system: Ax + by +cz =j Dx + ey + fz = k Gx + hy + iz = l

13
Example problem :D 5x + 5y + 7z = 21 5x + 7y + 9z = 23 7x + 9y + 11z = 25

14
Intimidating? Very…… but also very easy to solve! :D first get rid of the variables, literally forget about them so that it looks like 5 + 5 + 7 = 21 5 + 7 + 9 = 23 7 + 9 + 11 = 25 From here go to your calculator and press the 2 nd button and then hit x^-1. After you do this press the right arrow until you reach edit.

15
For the sake of understanding this we are going to pick to edit the letter A From here make it a 3 by 3 matrix and put in the values it should end up looking like this [5, 5, 7] [5, 7, 9] [7, 9, 11] After this we are going to hit the 2 nd button and the x^-1 button again (Remember hit 2 nd first before hitting x^-1 otherwise you will mess everything up). From here go to EDIT and pick B This time make it a 3 by 1 matrix and make it look like [21] [23] [25]

16
We are almost done now……. WEWTNESS!!!! :D from here simply hit 2 nd and go to x^-1 and instead of going to edit just press the number 1 and from here press x^-1 WITHOUT PRESSING THE 2 nd BUTTON LEAVE THAT ALONE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! After you have done that press enter and you should get [.5, -1,.5] [-1, -.75, 1.25] [.5, 1.25, -1.25] from here multiply this by the matrix B to get [-14.625] [-18.875] [24.5] And from here you have your answers to the variables x, y and z x= -14.625 y = -18.875 z= 24.5

Similar presentations

Presentation is loading. Please wait....

OK

Systems of Equations: Substitution Method

Systems of Equations: Substitution Method

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Antibiotic slides ppt on diabetic foot ulcer Ppt on trade fair circular Ppt on 2nd world war year Ppt on object-oriented programming c++ Ppt on life and works of william shakespeare Ppt on brain machine interface Ppt on revolt of 1857 lord Ppt on 13th finance commission Ppt on elements of a story Free ppt on personality development for students