review: 6.1 solving by graphing: remember: to graph a line we use the slope intercept form: y = mx...

REVIEW: 6.1 Solving by Graphing:

Remember:

To graph a line we use the slope intercept form:

y = mx +b

Slope = = STARING POINT (The point where it crosses the y-axis)

System Solution: The point where the two lines intersect (cross):

(1, 3)

Remember: What are the requirements

for this to happen?

REVIEW: 6.2: Solving by Substitution:

1): Isolate a variable2): Substitute the variable into the other equation3): Solve for the variable

4): Go back to the original equations, substitute, solve for the second variable

0): THINK - Which variable is the easiest to isolate?

5): Check

6.3: Solving by Elimination:

1): Pick a variable to eliminate

2): Add the two equations to Eliminate a variable3): Solve for the remaining variable

4): Go back to the original equation, substitute, solve for the second variable.

0): THINK: Which variable is easiest to eliminate.

5): Check

NOTE:

We can solve system of equations using a graph, the substitution or eliminations process.

The best method to use will depend on the form of the equations and how precise we want the answer to be.

CONCEPT SUMMARY: METHOD WHEN TO USE

Graphing When you want a visual display of the equations, or when you want to estimate the solution.

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YOU TRY IT:

Solve the system by Graphing:

{−2 𝑥+𝑦=26 𝑥+2 𝑦=14

YOU TRY IT: (SOLUTION)

{ −2 𝑥+𝑦=2→𝐘=𝟐𝐗+𝟐6 𝑥+2 𝑦=14→𝒀=−𝟑𝑿+𝟕

(1,4)

CONCEPT SUMMARY: METHOD WHEN TO USE

Substitution When one equation is already solved:y=mx+b or x= ym+b .

2 7 2

2

x

y x

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http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/fast-systems-of-equations/v/solving-linear-systems-by-substitution?exid=systems_of_equations

YOU TRY IT:

Solve the system by Substitution:

{−2 𝑥+𝑦=26 𝑥+2 𝑦=14

YOU TRY IT:(SOLUTION)

{−𝟐𝒙+𝒚=𝟐→ 𝐲=𝟐𝐱+𝟐

6 𝑥+2 𝑦=146 𝑥+2(2 𝑥+2)=146 𝑥+4 𝑥+4=14 x = 1y=2 (1 )+2→4

(𝟏 ,𝟒)

CONCEPT SUMMARY: (continue)METHOD WHEN TO USE

Elimination When the equations are in Ax +By = C form or the coefficients of one variable are the same and/or opposites

2 5 17

6 5 9

x y

x y

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http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/fast-systems-of-equations/v/solving-systems-of-equations-by-elimination

YOU TRY IT:

Solve the system by Elimination:

{−2 𝑥+𝑦=26 𝑥+2 𝑦=14

YOU TRY IT: (SOLUTION)

{−𝟐 𝒙+𝒚=𝟐→−𝟐(−𝟐 𝒙+𝒚=𝟐)𝟔 𝒙+𝟐𝒚=𝟏𝟒

{𝟒 𝒙−𝟐 𝒚=−𝟒𝟔 𝒙+𝟐𝒚=𝟏𝟒

10 x = 1

+

y = 4

ADDITIONALLY: System of equations help us solve real world problems.

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VIDEO-Word Prob.

NOTE:

We can solve system of equations using a graph, the substitution or eliminations process.

The best method to use will depend on the form of the equations and how precise we want the answer to be.

6.4 Application of Linear Systems:Break-Even Point: The point for business is where the income equals the expenses.

GOAL:

MODELING PROBLEMS: Systems of equations are useful to for solving and modeling problems that involve mixtures, rates and Break-Even points.Ex: A puzzle expert wrote a new sudoku puzzle book. His initial costs are $864. Binding and packaging each book costs $0.80. The price of the book is $2.00. How many books must be sold to break even?

SOLUTION:1) Write the system of equations described in the problem.

Income: y = $2x

Let x = number of books soldLet y = number of dollars of expense

or income

Expense: y = $0.80x + 864

SOLUTION: (Continue)2) Solve the system of equations for the break-even point using the best method.

$0.80x + 864 = $2x

To break even we want: Expense = Income

864 = 2x -0.80x 864 = 1.2x 720 = x

There should be 720 books sold for the puzzle expert to break-even.

YOU TRY IT:

Ex: A fashion designer makes and sells hats. The material for each hat costs $5.50. The hats sell for $12.50 each. The designer spends $1400 on advertising. How many hats must the designer sell to break-even?

SOLUTION:1) Write the system of equations described in the problem.

Income: y = $12.50x

Let x = number of hats soldLet y = number of dollars of expense

or income

Expense: y = $5.50x + $1400

SOLUTION: (Continue)2) Solve the system of equations for the break-even point using the best method.

$5.50x + $1400 = $12.50x

To break even we want: Expense = Income

1400 = 12.5x -5.50x 1400 = 7x 200 = x

There should be 200 hats sold for the fashion designer to break-even.

VIDEOS:Special Linear

Equations

https://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/fast-systems-of-equations/v/special-types-of-linear-systems

CLASSWORK:

Page 386-388

Problems: As many as needed to master the

concept.

SUMMARY:

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