![Page 1: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/1.jpg)
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)
![Page 2: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/2.jpg)
System Solution: The point where the two lines intersect (cross):
(1, 3)
![Page 3: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/3.jpg)
Remember: What are the requirements
for this to happen?
![Page 4: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/4.jpg)
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
![Page 5: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/5.jpg)
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
![Page 6: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/6.jpg)
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.
![Page 7: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/7.jpg)
CONCEPT SUMMARY: METHOD WHEN TO USE
Graphing When you want a visual display of the equations, or when you want to estimate the solution.
http://player.discoveryeducation.com/index.cfm?guidAssetId=8A6198F2-B782-4C69-8F6D-8CD683CAF9DD&blnFromSearch=1&productcode=US
![Page 8: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/8.jpg)
YOU TRY IT:
Solve the system by Graphing:
{β2 π₯+π¦=26 π₯+2 π¦=14
![Page 9: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/9.jpg)
YOU TRY IT: (SOLUTION)
{ β2 π₯+π¦=2βπ=ππ+π6 π₯+2 π¦=14βπ=βππΏ+π
(1,4)
![Page 10: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/10.jpg)
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
http://player.discoveryeducation.com/index.cfm?guidAssetId=A9199767-40AB-4AD1-9493-9391E75638D0
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
![Page 11: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/11.jpg)
YOU TRY IT:
Solve the system by Substitution:
{β2 π₯+π¦=26 π₯+2 π¦=14
![Page 12: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/12.jpg)
YOU TRY IT:(SOLUTION)
{βππ+π=πβ π²=ππ±+π
6 π₯+2 π¦=146 π₯+2(2 π₯+2)=146 π₯+4 π₯+4=14 x = 1y=2 (1 )+2β4
(π ,π)
![Page 13: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/13.jpg)
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
http://player.discoveryeducation.com/index.cfm?guidAssetId=02B482AE-EB9F-4960-BC5C-7D2360BDEE66
http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/fast-systems-of-equations/v/solving-systems-of-equations-by-elimination
![Page 14: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/14.jpg)
YOU TRY IT:
Solve the system by Elimination:
{β2 π₯+π¦=26 π₯+2 π¦=14
![Page 15: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/15.jpg)
YOU TRY IT: (SOLUTION)
{βπ π+π=πββπ(βπ π+π=π)π π+ππ=ππ
{π πβπ π=βππ π+ππ=ππ
10 x = 1
+
y = 4
![Page 16: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/16.jpg)
ADDITIONALLY: System of equations help us solve real world problems.
http://player.discoveryeducation.com/index.cfm?guidAssetId=A9199767-40AB-4AD1-9493-9391E75638D0
VIDEO-Word Prob.
![Page 17: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/17.jpg)
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.
![Page 18: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/18.jpg)
6.4 Application of Linear Systems:Break-Even Point: The point for business is where the income equals the expenses.
![Page 19: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/19.jpg)
GOAL:
![Page 20: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/20.jpg)
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?
![Page 21: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/21.jpg)
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
![Page 22: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/22.jpg)
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.
![Page 23: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/23.jpg)
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?
![Page 24: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/24.jpg)
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
![Page 25: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/25.jpg)
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.
![Page 26: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/26.jpg)
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
![Page 27: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/27.jpg)
CLASSWORK:
Page 386-388
Problems: As many as needed to master the
concept.
![Page 28: REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)](https://reader034.vdocument.in/reader034/viewer/2022051819/5517c1e555034616658b47e7/html5/thumbnails/28.jpg)
SUMMARY:
http://www.bing.com/videos/search?q=SYSTEM+OF+EQUATIONS+&view=detail&mid=2CFE63B47EDB353AFDCF2CFE63B47EDB353AFDCF&first=0&FORM=NVPFVR