lecture 6.1 6.2 bt
TRANSCRIPT
Today’s Agenda
Attendance / Announcements
Collect Projects
Return Exams
Sections 6.1, 6.2
Quiz Friday
Exam Schedule
Exam 4 (Ch 6,7)
Fri 11/15
Exam 5 (Ch 10)
Thur 12/5
Final Exam (All)
Thur 12/12
Review: Graphing/Equations of
Lines
Sections 2.1, 2.2
Systems of Linear Equations
A solution of a system of linear
equations is an ordered pair that
satisfies both equations.
12
93
yx
yx
Solve by Graphing
12
93
yx
yx
So, the
solution of
the system
is (2, -3)
Solve by Graphing
2
842
21 xy
yx
So, the
solution of
the system
is ?
Solve by Graphing
642
32
yx
yx
So, the
solution of
the system
is ?
Solve by Graphing
Solving Systems Algebraically
The Substitution Method
• Works well when it is easy to solve
for one of the variables
• Substitute expression into other
equation, Solve.
• Plug solved value back into either
equation to find solution.
• Check the solution in both equations
The Substitution Method
2356
63
yx
yx
• What does this tell us about the
graphs of the system?
The Substitution Method
762
93
xy
yx
• What does this tell us about the
graphs of the system?
The Substitution Method
428
24
yx
yx
• What does this tell us about the
graphs of the system?
The Substitution Method
52
32
yx
yx
• What does this tell us about the
graphs of the system?
Solving Systems Algebraically
The Elimination Method
• We can multiply/divide any linear
equation.
• We can also add/subtract linear
equations together.
• Use algebra to eliminate one of the
variables, solve for the other.
• Check the solution in both equations
The Elimination Method
123
45
yx
yx
Addition Method
- Want to get
“opposite
coefficients”
- Then add
equations to
eliminate variable
Subtraction
Method
- Want to get
“same
coefficients”
- Then subtract
equations to
eliminate variable
The Elimination Method
1232
232
xy
yx
Want to rewrite to line up like
terms
The Elimination Method
267
1452
yx
yx
Applications
The sum of two numbers is 70 and
their difference is 24. Find the two
numbers.
Solving Larger Systems using
Substitution
• Use algebra to isolate one of the
variables, substitute into the other
two.
• Solve the two variable system, use
Substitution find the first variable
• Check solution in all three equations
The Substitution Method
2
123
22
zyx
zyx
zyx
The Substitution Method
723
164
232
zyx
zyx
yx
The Substitution Method
2242
22
52
zyx
zyx
zyx
Classwork / Homework
• Page 317
•1 – 15 odd, 19
• Page 329
•9, 39, 41, 45