Download CLASSWORK REVIEW WARM-UP TODAY’S OBJECTIVE

CLASSWORK REVIEW
WARM-UP
t
1. Is the point (0,3) a solution for
this system of inequalities?
Let t = number of regular 22000
tickets
20000
x  y  2

3 x  2 y  6
Let s = number of student16000
discount tickets
70t  20 s  500, 000

t  s  20, 000
12000
Yes
2. Solve this linear system.
800
0
400
0
s
y 3  x

 4 x  y  2
(1, 2)
TODAY’S OBJECTIVE
• To solve a system with three
variables
• Use the graphing calculator
3-5 SYSTEMS
WITH THREE
VARIABLES
USING THE
CALCULATOR TO SOLVE
SYSTEMS
• We can use amatri
_______ to represent
a system of equations
x
• Matrix -A rectangular array of
numbers
3 4 2 
6 1 7   A


1 3 
9 4   B


IDENTIFYING A
MATRIX ELEMENT
• Matrix ElementEach
- number in a
matrix
• Look at the row and column
numbers
• Notation identifies a particular
3
element in a matrix
columns
a12 Is the element in row 1
and column 2
2x3
Matrix
2 rows
3 4 2 
6 1 7   A


1
IDENTIFYING A
MATRIX ELEMENT
GRAPHING
CALCULATORS
Identify the indicated element.
A)
B)
a 21
C)
a13
a 22
7
1
2
3 9 1
A   2 7 6 
1 4 8 
7
 5 
 
Matrix of Matrix
coefficient of
constan
s
ts
Number of
rows =
Number of
equations
Number of
columns = 1
REPRESENT A SYSTEM
USING
MATRIX
2  x    7 
 4A 
3

 4 2 
3 1A


1   y    5
x 
 y  X
 
AX  B
X  A1 B
X
 4 2 
3 1


1
7
 5 
 
• One for the coefficients
4 x  2 y  7
3 x  1 y  5
4 x  2 y  7
3 x  1 y  5
 4 2 
3 1


• To use it, we need to create 2 matrices
• Another for the constants
REPRESENT A SYSTEM
USING A MATRIX
Number of
rows =
Number of
equations
Number of
variables =
Number of
columns
• We can use the graphing calculator to
solve linear systems
7
 5  B
 
REPRESENT A SYSTEM
USING A MATRIX
4 x  2 y  7
3 x  1 y  5
 4 2   x    7 
 3 1   y    5

 
 
1. Write each equation
with variables in the
same order. Put
variables on one side of
the equation, constants
on the other
2. Write a matrix with
coefficients of the linear
system.
3. Write a matrix with the
constants of the linear
system.
REPRESENT A SYSTEM
USING A MATRIX
4 x  2 y  7
3 x  1 y  5
1
x 
 4 2   7 
 y  

 
 
 3 1   5 
Matrix of Matrix
coefficient of
constan
s X  A1 B
ts
2
PRACTICE
PROBLEMS
1. x  2 y  16
PRACTICE
PROBLEMS
2. 7 x  y  6
7 x  y  6
3x  y  8
1 2  1 16 
3 1 
8


 
 7 1
 7 1 


1
6
 6 
 
Infinitely Many
Solutions
(0,8)
SYSTEMS WITH 3
VARIABLES
 x  y  z  1

 x  y  3 z  3
2 x  y  2 x  0

x  y  z  1
x  y  3 z  3
2 x  0 y  4 z  4
1. Eliminate y by
adding equations 1
and 2
x  y  3 z  3
2x  y  2z  0
3 x  0 y  5 z  3
2. Eliminate y by
adding equations 2
and 3
SYSTEMS WITH 3
VARIABLES
x  y  z  1
4  y  3  1
1  y  1
y2
5. Substitute the xvalue and z-value into
one of the original
equations.
3. 1x  2 y  1z  1
2 x  1z  9
3 x  1 y  3
 1 2 1 1 1 
 2 0 1  9 

  

 3 1 0   3
(2,3,5)
4.  x  4 y  6 z  21

2 x  2 y  z  4
8 y  z  1

4 6  1 21
1
 2 2 1 


 0 8 1 
 
4 
 
 1
(1,.5,3)
SYSTEMS WITH 3
VARIABLES
(2 x  4 z  4 ) 3
( 3x  5 z  3 )2
6 x  12 z  12
6 x  10 z  6
2 z  6
z  3
2 x  4 z  4
2 x  4(3)  4
2 x  12  4
x4
3. Write the two new
equations as a system.
Eliminate x and solve
for z
4. Substitute the value
for z into one equation
in the two variable
system. Solve for x
TONIGHT’S
HOMEWORK
Page 179; 12, 15, 18, 21, 32 - 37
The solution is (4, 2, -3)
3