Section 9.3 Systems of Linear Equations in

Several VariablesObjectives:•Solving systems of linear equations using Gaussian elimination.

Ex 1. Solve the system using Gaussian elimination.

Equation 1

Equation 2

Equation 3

2 3 12 13

3 2 5 3

x y zx y zx y z

Ex 2. Solve using Gaussian elimination.

2 3 12 13

2 4 7 11

x y zx y zx y z

Class Work

1. Solve using Gaussian elimination.2 2

3 5 82 2 7

x y zx y zx y z

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.

2 2 12 2 63 4 3 5

x y zx y zx y z

Ex 4 Solve the system using Gaussian elimination.

5 22 4 22 4 2 8

x y zx y zx y z

Class Work

Solve using Gaussian elimination.2. 3.

5 23 3 23 9 21 18

x y zx y zx y z

3 60

2 5 3

x yx y zx y z

Class Work

4.

2 83

2 4 18

x y zx y zx z

HW p658 17 - 25 odd, 33