Unit 5 systems of equations and inequalities answer key

ALGEBRA 1UNIT 5SYSTEMS OF EQUATIONS AND INEQUALITIESUnit Essential QuestionsHow does graphing help you solve a system of equations?How does writing equivalent equations help you solve a systemof equations?

SOLVING SYSTEMSBY GRAPHINGA-REI.C.6:Solve systems of linear equations exactly andapproximately (e.g. with graphs), focusing on pairs of linearequations in two variables.

KEY CONCEPTS AND VOCABULARYSystem of Equations- a set of two or more equations that use thesame variables.System of Linear Equations- when the graph of each equation of asystem is a line.Solution to a System of Equations– a set of values for the variablesthat makes all the equations true.

GraphNumber ofSolutionsName of SystemSlopes are…y-interceptsare…1IndependentSlope aredifferenty-intercepts canbe the same ordifferent0InconsistentSlope are thesamey-intercepts aredifferentInfiniteDependentSlopes are thesamey-intercepts arethe sameKEY CONCEPTS ANDVOCABULARY

Graph each system and determine the number of solutions.If ithas one solution, find the one solution.a)b)c)EXAMPLE 1:SOLVING SYSTEMS BY GRAPHINGOne solution;One Solution; (2, 0)Infinite Solutionsy=-x+3y=2x-3ìíïîïy=-2x+4y=x-2ìíïîïy=3x+7-2y+6x=-14ìíïîï53,13æèçöø÷

Graph each system and determine the number of solutions.If ithas one solution, find the one solution.SOLVING SYSTEMS BY GRAPHINGìíïîïx+y=4íïîïíïîïd)e)f)=-x+1+4y=-12EXAMPLE 1:SOLVING SYSTEMS BY GRAPHINGìíïîïx+y=4íïîïíïîïy=-x+1+4y=-12ìíïîïíïîïx+4y=-12ìíïîï

Get answer to your question and much more

EXAMPLE 2:WRITING AND SOLVING SYSTEMS FOR REAL WORLDSITUATIONSMulan and Lilo are competing to see who can sell the most candybars for a fundraiser.Mulan sold 4 candy bars on the first day and 2each day after that.Lilo sold 7 on the first day and 1 each day afterthat.a)Write an equation for the number of candy bars each person sold.b)Graph each equationc)Solve the system.Interpret your solution

Get answer to your question and much more

SOLVING SYSTEMSUSING SUBSTITUTIONA-REI.C.6:Solve systems of linear equations exactly andapproximately (e.g. with graphs), focusing on pairs of linearequations in two variables.

Do NowList the basic steps needed to solve systems ofequations by graphing.

KEY CONCEPTS AND VOCABULARYSubstitution– means to plug in or replace a variable with anexpression.

Upload your study docs or become a

Course Hero member to access this document

Upload your study docs or become a

Course Hero member to access this document