10.3 Day 1 Systems of Linear Equations ­ Determinants
January 07, 2011
10.3 Systems of Linear Equations: Determinants DAY 1
Objectives:
1. Evaluate 2 by 2 determinants.
2. Use Cramer's Rule to solve a system of two equations containing two variables. Nov 9­12:29 PM
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10.3 Day 1 Systems of Linear Equations ­ Determinants
January 07, 2011
Guess what??
...today we are learning another way to solve a system of linear equations called
CRAMER'S RULE!
...AND it can only be used when the # of equations equals the # of variables!
Jan 6­10:32 AM
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10.3 Day 1 Systems of Linear Equations ­ Determinants
January 07, 2011
Determinants
This is a 2 by 2 determinant.
a b
D = c d
Why do you think it's called a 2 by 2 determinant?
Jan 6­11:02 AM
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10.3 Day 1 Systems of Linear Equations ­ Determinants
January 07, 2011
Determinants
This is how you find the value of a 2 by 2 determinant.
a b
D = = ad ­ bc
c d
EASY...try this one!
Example: Evaluate
3 ­2
6 1
Jan 6­11:02 AM
4
10.3 Day 1 Systems of Linear Equations ­ Determinants
January 07, 2011
Cramer's Rule Given the following system of equations:
{
ax + by = s
cx + dy = t
You find x and y by using determinants.
Dx
x = D
Dy
y = D
What can D not equal??
More details about D, Dx, and Dy on the next page...
Nov 30­12:42 PM
5
10.3 Day 1 Systems of Linear Equations ­ Determinants
January 07, 2011
Cramer's Rule Given the following system of equations:
{
ax + by = s
cx + dy = t
You find x and y by using determinants.
Dx
x = D
Dy
y = D
D = a b
c d
D ≠ 0
Nov 30­12:42 PM
6
10.3 Day 1 Systems of Linear Equations ­ Determinants
January 07, 2011
Cramer's Rule Given the following system of equations:
{
ax + by = s
cx + dy = t
You find x and y by using determinants.
Dx
x = D
Dy
y = D
s b
Dx = t d
s
Dy = ca t
Nov 30­12:42 PM
7
10.3 Day 1 Systems of Linear Equations ­ Determinants
January 07, 2011
's Rule Given the following system of equations:
{
ax + by = s
cx + dy = t
You find x and y by using determinants.
Dx
x = D
Dy
y = D
s b
t d
x = a b
c d
a s
c t
y = a b
c d
Nov 30­12:42 PM
8
10.3 Day 1 Systems of Linear Equations ­ Determinants
January 07, 2011
Cramer's Rule {
ax + by = s
cx + dy = t
Dx
x = D = s b
t d
a b
c d
Dy
= y = D
a s
c t
a b
c d
Try this one...I promise it's not that hard!!
{6x + y = 13
Example: 3x ­ 2y = 4
x = 2
y = 1
Nov 30­12:42 PM
9
10.3 Day 1 Systems of Linear Equations ­ Determinants
January 07, 2011
Cramer's Rule {
ax + by = s
cx + dy = t
Dx
x = = D
s b
t d
a b
c d
D
y = Dy = a s
c t
a b
c d
ONE MORE!!
{­3x ­ 2y = 0
Example: 6x + 4y = 5
NOT
APPLICABLE
Nov 30­12:42 PM
10
10.3 Day 1 Systems of Linear Equations ­ Determinants
January 07, 2011
Homework:
page 767 (5 ­ 10, 15 ­ 26)
Jan 6­2:44 PM
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Attachments
Circumcenter_﴾Perp._Bisectors﴿.gsp