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Chapter 6.1
Common Core – A.REI.6 Solve systems of linear
equations exactly and approximately, focusing on
pairs of liner equations in two variables.
Objectives – To solve systems of equations by
graphing. To analyze special systems.
Ch 6.1 Notes
Solving two equations two unknowns by Graphing
One Solution
(They Cross)
Infinitely Solutions No Solution
(Same Line)
(Parallel Lines)
Chapter 6.2
Common Core – A.REI.6 Solve systems of
linear equations exactly and approximately,
focusing on pairs of liner equations in two
variables.
Objectives – To solve systems of equations by
using substitution.
Ch 6.2 Notes
Solving two equations two unknowns by Substitution
1) Take an equation and either solve for X or Y
2) Plug it into the other equation and solve.
3) Substitute it back into the original equation to
solve for the other variable.
Solve y = 3x
x + y = -32
Chapter 6.3
Common Core – A.REI.5 & A.REI.6 Prove that,
given…two equations…replacing one equation by
the sum of that equation and a multiple of the other
produces a system with the same solutions.
Objectives – To solve systems by adding or
subtracting to eliminate a variable.
Ch 6.3 Notes
Solving two equations two unknowns by Elimination
1) Eliminate the X or Y variable by making
them opposites of each other and then
add the two equations up.
2) Substitute the answer into either equation
to solve for the other variable.
Solve 2x + 5y = 17
6x – 5y = -9
Solve 5x – 6y = -32
-3x – 6y = -48
Solve -2x + 15y = -32
7x - 5y = 17
Solve 3x + 2y= 1
4x + 3y = -2
Chapter 6.4
Common Core – A.REI.6 Solve
systems of linear equations exactly and
approximately, focusing on pairs of
liner equations in two variables.
Objectives – To choose the best
method for solving a system of linear
equations.
Ch 6.4 Notes
Applications of Linear Systems
Finding a Break Even Point
A Fashion designer makes and sells hats. The material
for each hat costs $5.50. The hats sell for $12.50. The
designer spends $1400 on advertising. How many hats
must the designer sell to break even?
Identifying Constraints and Viable Solutions
The local zoo is filling two water tanks for the elephant
exhibit. One water tank contains 50 gal. of water and is
filled at a constant rate of 10 gal/h. The second water
tank contains 29 gal of water and is filled at a constant
rate of 3 gal/h. When will the two tanks have the same
amount of water?
Solving a Wind or Current Problem
Plane A flies from Charlotte, North Carolina, to Los
Angeles, California at a rate of 495 mi/h with a
headwind. At the same time, Plane B flies form Los
Angeles to Charlotte at a rate of 550 mi/h with a
tailwind. The air speed of each plane is the same. The
ground speeds are shown below. What is the air
speed? What is the wind speed?
Chapter 6.5 and 6.6
Common Core – A.REI.12 & A.CED.3 Graph the
solutions to a linear inequality in two variables
as a half-plane.
Objectives – To graph linear inequalities in two
variables. To use linear inequalities when
modeling real-world situations. To solve
systems of linear inequalities by graphing. To
model real-world situations using systems of
linear inequalities.
Ch 6.5 and 6.6 Notes
Graphing Linear Inequalities
1) Graph the lines
< or > use a dotted line
< or > use a solid line
2) Shade above or below, or left or right of the
line by picking a point and seeing if it works
in the inequality.