Download presentation

Published byLiliana Copeland Modified over 6 years ago

1
**3.5 Solving Systems of Equations in Three Variables**

Objectives: 1. Solve system of linear equations in three variables.

2
**Systems in Three Variables**

The graph of an equation in 3 variables where all variables are to the first power is a plane. The solution to a system with 3 equations and 3 variables is an ordered triple. Ordered Triple – (x, y, z) Three possible solutions – one solution, no solution and infinitely many solutions. Solve by substitution or elimination.

3
Example Use 1st and 3rd equations to eliminate z 5x+3y+2z=2 5x+3y+2z=2 x+4y+2z=16 -x-4y-2z=-16 4x-y=-14 Use 2nd and 3rd to eliminate z again. (mult 1st by 2) 2x+y-z=5 4x+2y-2z=10 x+4y+2z=16 x+4y+2z=16 5x+6y=26 Use these 2 equations to eliminate x or y. Solve 5x+3y+2z=2 2x+y-z=5 x+4y+2z=16 Use two pairs of equations to create a system of 2 equations with 2 unknowns.

4
Continued Use the x and y you found to find z. Plug into any of the original equations. 5x+3y+2z=2 5(-2)+3(6)+2z= z=2 8+2z=2 2z=-6 z=-3 Solution: (-2, 6, -3) 4x-y=-14 5x+6y=26 Multiply 1st equation by 6 24x-6y=-84 29x=-58 x=-2 Plug in to find y 4(-2)-y= y=-14 -y=-6 y=6

5
Another Example -x-3y=19 -3x-9y=57 Multiply 1st by -3 to eliminate y 3x+9y=-57 0=0 Infinitely many solutions x-2y+z=8 2x+y+z=-11 3x-6y+3z=24 x-2y+z=8 x-2y+z=8 2x+y+z=-11 -2x-y-z=11 -x-3y=19 2x+y+z=-11 -6x-3y-3z=33 3x-6y+3z=24 3x-6y+3z=24 -3x-9y=57

6
Try one Multiply 2nd by 4 3y-4z=25 16y+4z=32 19y=57 y=3 3(3)-4z=25 9-4z=25 -4z=16 z=-4 x+6(3)+(-4)=20 x+14=20 x=6 Solution: (6, 3, -4) x+2y=12 3y-4z=25 x+6y+z=20 x+2y=12 -x-2y=-12 x+6y+z=20 x+6y+z=20 4y+z=8 Use this with the second equation

7
**Homework page 142 13-21 odd (5 problems!)**

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google