Fontana Unified School DistrictEvery Student Successful Engaging Schools Empowered CommunitiesOffline Distance LearningSecondaryAdvanced Math 7May 2020School Name:Student ID#:Math Teacher Name:Period:May 2020
May 2020
Advanced Math 7: May 4 β May 8Concept: Solving Systems by GraphingSystems of linear equations- A set of two or more linear equations with the samevariablesSolutions to systems of linear equations- A solution to a system of equations is anordered pair that is true for both equations-When you graph a system, the solution iswhere the two lines intersectOften, the system will be marked with bracketslike above left example, but it is not required.-When you graph a linear system, you graph bothlines on the same coordinate plane.One SolutionInfinite SolutionsNo Solutions-The system will have onesolution when the lines crossexactly one time.-The system will have aninfinite number of solutionswhen the lines are the same,or they touch at every point.-The system will have nosolutions if the lines neverintersect at any point.-Here, the solution is (15, 9)because that is where the linesintersect.-These lines fall on top of eachother, so there is an infinitenumber of solutions.These lines will have thesame slope and the same yintercept.-These lines will neverintersect, so they have nosolution.These lines will have thesame slope but different yintercepts.-Ex.π¦π¦ 2π₯π₯ 2π¦π¦ 2π₯π₯ 2-Ex.π¦π¦ 3π₯π₯π¦π¦ 3π₯π₯ 6May 2020
Checking SolutionsChecking Solutions for a System--Substitute the coordinate pair the equation, if it istrue, then it is a solutionSolving by GraphingIf the coordinate pair is a solution to a systemof equations, then it must be true for BOTHequationsSolving by Graphing: Not in ππ ππππ ππ1) Find the slope and y-intercept1) The first thing you need to is solve eachequation for y.2) Graph both lines and identify where theyintersect.2) Then itβs the same steps as before β grapheach line and determine whether theyintersect.3) Check your solution for both equations3) Check each solution to determine if it istrue.May 2020
Problems:1. Determine if (3, 4) is a solution to the system.2π₯π₯ π¦π¦ 2π₯π₯ 2π¦π¦ 113. Identify the solution to the system.The solution is ( , ).5. How many solutions does these systems ofequations have? Justify how you know.2. Determine if (3, -1) is a solution to thesystem.π¦π¦ 3π₯π₯ 1π¦π¦ 2π₯π₯4. Identify the solution to the system.The solution is ( , ).6. Describe the difference in the number ofsolutions between a system of linearequations that coincide and a system of linearequations that are parallel.May 2020
7. Graph the system and identify the solution.8. Graph the system and identify the solution.π¦π¦ 3π₯π₯ 2π¦π¦ 2π₯π₯ 32π₯π₯ 2π¦π¦ 64π₯π₯ 6π¦π¦ 129. Graph the system and identify the solution.10. Graph the system and identify the solution.π¦π¦ 3π₯π₯ 2π¦π¦ 3π₯π₯ 2π¦π¦ 2π₯π₯ 12π¦π¦ 4π₯π₯ 2May 2020
Advanced Math 7: May 11 β May 15Concept: Solving Systems AlgebraicallySolving Systems AlgebraicallySubstitution---Solving a system by substitution is where yousubstitute a value or expression from the firstequation into the second equation to solve for oneof the variables.You need to have one equation by in βy β or βx β form.--π¦π¦ 3π₯π₯ 42π₯π₯ 3π¦π¦ 7The first equation is set up as y , which meanswe can substitute the 3x - 4Substitution Example-Elimination2π₯π₯ π¦π¦ 11π¦π¦ 3π₯π₯ 9The second equation has a y , so I take the 3x β9 and substitute it for the y in the first equation.2π₯π₯ ( ) 11---Now I solve for x.2π₯π₯ 3π₯π₯ 9 115π₯π₯ 9 115π₯π₯ 20π₯π₯ 4Substitute the x back into any equation. Iβmchoosing the second one because it seems like itwill be easier to find y.π¦π¦ 3(4) 9π¦π¦ 12 9π¦π¦ 32π₯π₯ 3π¦π¦ 12π₯π₯ 3π¦π¦ 15We have -3y in the first equation and 3y in thesecond equation, so they add up to 0Elimination Example-2π₯π₯ 3π¦π¦ 20 2π₯π₯ π¦π¦ 4I see that I have a -2x and 2x in my twoequations, so that is the variable I will βeliminateβor make 0.2π₯π₯ 3π¦π¦ 20 2π₯π₯ π¦π¦ 4π¦π¦ 3π₯π₯ 92π₯π₯ (3π₯π₯ 9) 11Solving a system by elimination is where you lineup both equations and add or subtract themtogether to eliminate one variable completely (itadds up to 0), allowing you to solve for the othervariable.You need one set of coefficients to be opposite ofeach other ( -4 and 4 or -1 and 1)--0 4π¦π¦ 24From there, I solve for y.4π¦π¦ 24π¦π¦ 6I substitute the 6 back into either equation tosolve for x. Iβm choosing the first one.2π₯π₯ 3(6) 202π₯π₯ 18 202π₯π₯ 2π₯π₯ 1The solution to the system is (1, 6).The solution to the system is (4, 3).May 2020
Setting a Problem up for SubstitutionSetting a Problem up for Elimination--If a problem isnβt set up for substitution, movethings around until you have anπ₯π₯ ππππ π¦π¦ If there arenβt any coefficients that are alreadyopposites, you can multiple one entire equation tocreate opposites.(3, 2)(2, 2)The Variable Disappeared!-There are two situations where we get an answer that makes the algebra look strange, meaning thevariable disappears completely or you end up with something like x x.-When we solve for an infinite number of solutions, it will look like this:1 1-When we solve for no solutions, it will look like this:1 2Infinite SolutionsNo Solutions-We know what the graph looks like, now we willlearn what the algebra looks like.-We know what the graph looks like, now we willlearn what the algebra looks like.-Iβve substituted an expression and I get a problemthat looks like this:-Iβve substituted an expression and I get a problemthat looks like this:--2π₯π₯ 3 2π₯π₯ 3After subtracting 2x from each side, I get this:3 3This is true. This is always true. So, this systemwill have an infinite number of solutions.2π₯π₯ 1 2π₯π₯ 3-After subtracting 2x from each side, I get this:-1 3This is not true. This is never true. So, thissystem will have no solutions.May 2020
Infinite Solutions Exampleπ¦π¦ 2π₯π₯ 32π¦π¦ 4π₯π₯ 62(2π₯π₯ 3) 4π₯π₯ 64π₯π₯ 6 4π₯π₯ 6 6 6There is an infinite number of solutions.No Solutions Example2π₯π₯ 3π¦π¦ 72π₯π₯ 3π¦π¦ 3I subtract the two equations to eliminate the variables0 40 does not equal 4. There are no solutions.Recap:May 2020
May 2020
Problems:1. Some systems of two linear equations in twovariables have a single solution (x, y). Othershave no solutions, while still others have aninfinite number of solutions.2. When solving systems algebraically, howmany solutions will each system have when Isolve for a variable and see this:Match each description to number of solutions.x 1Parallel lines2 2Intersecting linesCoinciding lines- Singlesolution-1 5- No solution-Infinitesolution3. Using substitution, solve the system.π₯π₯ 2π¦π¦ 18π₯π₯ 4π¦π¦5. Using elimination, solve the system.5π₯π₯ 2π¦π¦ 26 π₯π₯ 2π¦π¦ 224. Using substitution, solve the system.π₯π₯ 3π¦π¦ 22π₯π₯ π¦π¦ 106. Using elimination, solve the system.6π₯π₯ 6π¦π¦ 283π₯π₯ 3π¦π¦ 14May 2020
7. Which method makes more sense to solve thissystem? Why?8. Solve the system with your chosen method.9. Which method makes more sense to solve thissystem? Why?π¦π¦ 4π₯π₯π¦π¦ 4π₯π₯ 710. Solve the system with your chosen method.π¦π¦ 4π₯π₯π¦π¦ 4π₯π₯ 711. Solve the system with any method.12. Solve the system with any method.π₯π₯ π¦π¦ 143π₯π₯ π¦π¦ 36May 2020
Infinite Solutions - The system will have an infinite number of solutions when the lines are the same, or they touch at every point. - These lines fall on top of each other, so there is an infinite number of solutions. - These lines will have the sam
Engaging P-20W Stakeholders (PPT Presentation). Strategies for engaging Pβ20 stakeholders were discussed, including who is engaged and why, how stakeholders with varying backgrounds are engaged, roles and responsibilities of stakeholders, and lessons learned from engaging Pβ20 stakeholders. Engaging Postsecondary Stakeholders
Successful California Schools in the Context of Educational Adequacy American Institutes for Research Page v low-performing schools per student ( 7,799 vs. 8,021; the statewide average is 7,523). For both BTO and LP schools, total per pupil spending is positively correlated with povertyβhigh-
Dec 01, 2017Β Β· ORANGE COUNTY PUBLIC SCHOOLS SCHOOL WITHDRAWAL INFORMATION Student Withdrawal Process: *Any student (includes charter schools, exceptional education, McKay Scholarship, Alternative school, contract schools, technical schools and private schools) must have a withdrawal fo
Student Code of Conduct Every student succeeding Every student succeeding is the shared vision of Queensland state schools. Our vision shapes regional and school planning to ensure every student receives the support needed to belong to the school community, engage purposefully in learning and experience academic success.
Student Code of Conduct Every student succeeding Every student succeeding is the shared vision of Queensland state schools. Our vision shapes regional and school planning to ensure every student receives the support needed to belong to the school community, engage purposefully in learning and experience academic success.
Student Code of Conduct Every student succeeding Every student succeeding is the shared vision of Queensland state schools. Our vision shapes regional and school planning to ensure every student receives the support needed to belong to the school community, engage purposefully in learning and experience academic success.
This advice is for school leaders and governing bodies in all schools and proprietors of independent schools, and for local authorities. It covers thefollowing school types: maintained schools, maintained special schools, academies, free schools (including university technical colleges and studio schools
and pupils. Charter schools may consist of new schools or all or any portion of an existing school. Charter schools are public schools that serve as alternatives to traditional public schools and charter schools are not subject to the requirements of article XI, section 1, Constitution of Arizona, or chapter 16 of this title." A.R.S 15-181