Lecture 6.1 6.2 bt
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Transcript of Lecture 6.1 6.2 bt
Today’s Agenda
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MyMathLabs HW Due Sunday
Section 6.1, 6.2
Exam Schedule
Exam 5 (Ch 6.1, 7)
Wed 4/1
Exam 6 (Ch 10)
Monday 4/27
Final Exam (Cumulative)
Monday 5/4
Review: Graphing/Equations
of Lines
Sections 2.1, 2.2
Linear Equations
How can we solve this?
93 yx
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
123
45
yx
yx
The Elimination Method
1232
232
xy
yx
Want to rewrite to line up like terms
The Elimination Method
267
1452
yx
yx
Solving for three unknowns using
back substitution
2𝑥 − 𝑦 + 3𝑧 = 2𝑥 + 2𝑦 − 𝑧 = 6
−𝑥 − 𝑦 + 𝑧 = −5
Graphing Linear Inequalities
Graphing Linear Inequalities
𝑦 < 𝑥 + 3
1. Graph boundary line
3 xy
2. Check inequality sign
(Dashed or Solid?)
3. Shade accordingly
4. Test Points
Graphing Linear Inequalities
1. Graph boundary line
2
3
2
1 xy
2. Check inequality sign
(Dashed or Solid?)
3. Shade accordingly
4. Test Points
624 xy 23
21 xy
Classwork / Homework
•Page 317
•1 – 15 odd, 19, 26
•Page 395
•1 - 10