Download Using Transformations to Solve Linear Equations

Goal: Using
Transformations to Solve
Linear Equations
Agenda
Tuesday/Wednesday – Learn how to solve
equations with addition and subtraction (3.1).
Thursday/Friday – Learn how to solve equations
with multiplication and division (3.2).
Next Monday – Using both to solve multi-step
equations (3.3).
What’s a Linear Equation…in one
variable?
From the glossary – “An equation in which the variable is
raised to the first power and does not occur in a
denominator, inside a square root symbol, or inside an
absolute value symbol.” Essentially their graphs have
straight lines.
Some Examples:
x 1  4
3 1
q 
4 2
y  2  6 y  3 y  1
Some non-examples:
x4 5
x 1  4
2
y  2  6 x  2
x 1  4
Solving Equations…
Transformations
You will now solve equations using
“transformations”, which are a combination of
inverse operations used to isolate the variable
to one side of the equation.
Transformations may be one-step or multiplestep solutions.
Equations may also require simplification to
minimize the number of transformations.
Solving Equations…
Transformations
An equation is transformed when it is rewritten
to produce an equation with the same solutions
as the original equation. Such equations are
said to be “equivalent”.
Examples:
x42
and
x  2
and
x20
Solving Equations…
Transformations using Addition and
Subtraction
Examples:
Examples:
For 10.28.10 HW Do Problems:
Regular: pg. 135ff…4-12 (even);21-29 (odd);
42-46 (even); Fraction Practice – 2-8 (even);
17,20,26,27;
Advanced: pg.135ff…28-40(even); 49,52,53,55;
Fraction Practice – 5-8 (all); 18,21,27,30;
11.2.10 Warm-Up
11.2.10 - We’ve already seen how to solve
linear equations using transformations of
addition and subtraction…that is, inverse
operations and simplification. Now we
will…
Solve Linear Equations w/division and
multiplication (3.2).
Solve linear equations with multi-step
transformations (3.3).
Solve linear equations with variables on
both sides of equations (3.4).
Solving Equations…
Transformations using
Multiplication and Division
Examples – Div./Multi.
4n  24
1
 y  6
5
1
2
y5
3
3
Do Problems:
Pg. 142…39-43 (odd); 49-53 (odd); 58-59
Solving Multiple-Step
Equations…Warm-Up
Solving Multiple-Step Equations…
Solving Linear Equations may require two or
more transformations…here’s a simple
process to remember:
1.) Collect variables on “left side”; Or collect
variables on “right side” of equation.
2.) Simplify one or both sides of the equation
(if needed).
3.) Use inverse operations to isolate the
variable.
Solving Multiple-Step Equations…
Examples – Multi-Step:
1
30  16  x
5
7 x  4 x  9
4
 (2 x  4)  48
9
Do Problems:
Reg. Algebra: Pg. 148-9…25-37 (odd); 5054 (even)
Adv. Algebra: pg. 148-9…(33-39 odd); 6265 (all)
Solving Linear Equations: Variables
on Both Sides
Solving Linear Equations: Variables
on Both Sides
Examples:
Special Cases: Identities and No
Solutions
Collect Variables on Left Side or Collect
Variables on Right Side.
Odd cases: Identities and cases where
there is no solution.
Examples:
An Identity:
3(4  4 x)  12 x  12
No Solution:
12c  4  12c
Do Problems:
11.8.10 HW Reg. Algebra - Pg. 157…1,4-8
(even); 12-24 (even); 45,46,70
OR
Pg. 157…29-41 (odd), 47-49 (all);
Formulas and Functions
The ability to transform and solve
equations allows us to use formulas for
discovering new information from real-life
situations.
“A formula is an algebraic equation which
relates two or more real-life quantities.”
“An equation is in function form if one
variable is isolated on one side of the
equation.”
Formulas and Functions
Examples:
Al w
5
C  ( F  32)
9
D
R
T
I P r t
Acircle   r 2
Examples:
Do Problems:
11.8.10 HW Adv. Algebra – pg. 177…3-21
(odd); 37-42 (all)
OR
Pg. 177…11-29 (odd), 40-44 (all), 47-49 (all)