Transcript Ch. 9-3

Section 9.3
Systems of Linear Equations in
Several Variables
Objectives:
•Solving systems of linear equations
using Gaussian elimination.
Ex 1. Solve the system using Gaussian
elimination.
 x  2y  3z  1

 x  2y  z  13
3 x  2y  5z  3

Equation 1
Equation 2
Equation 3
Ex 2. Solve using Gaussian elimination.
x  2 y  3z  1
x  2 y  z  13
2 x  4 y  7 z  11
Class Work
1. Solve using Gaussian elimination.
x  y  2z  2
3x  y  5 z  8
2 x  y  2 z  7
Number of Solutions of a Linear System
For a system of linear equations, exactly one of
the following is true.
1. The system has exactly one solution.
2. The system has no solution.
3. The system has infinetly many solutions.
For a system to have exactly one solution we
have three planes intersecting in one point.
For a system to have no solutions the planes
have no point in common.
For a system to have infinitely many solutions
the three planes intersect in a line.
Ex 3. Solve the following system using Gaussian
elimination.
x  2 y  2z  1
2 x  2y  z  6
3 x  4 y  3z  5
Ex 4 Solve the system using Gaussian
elimination.
x  y  5 z  2
2 x  y  4z  2
2 x  4 y  2z  8
Class Work
Solve using Gaussian elimination.
2. x  y  5z  2
3. 3 x  y
3 x  y  3z  2
3 x  9 y  21z  18
6
x y z0
 x  2y  5z  3
Class Work
4. 2 x  y  z  8
x  y  z  3
2 x  4z  18
HW p658 17 - 25 odd, 33