 # Unit 1.2 – Solve Linear Systems by Graphing MM3A5c - Represent and solve realistic problems using systems of linear equations Essential Question: What.

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Unit 1.2 – Solve Linear Systems by Graphing MM3A5c - Represent and solve realistic problems using systems of linear equations Essential Question: What is a system of linear questions and how can we relate them to real world concepts?

Unit 1 – Algebra: Linear Systems, Matrices, & Vertex- Edge Graphs  1.2 – Solve Linear Systems by Graphing  Georgia Performance Standard:  MM3A5c – Represent and solve realistic problems using systems of linear equations. MM3A5c - Represent and solve realistic problems using systems of linear equations

Vocabulary  Systems of two linear equations  Solution of a System  Consistent  Inconsistent  Independent  Dependent MM3A5c - Represent and solve realistic problems using systems of linear equations

System of linear equations  A system of linear equations in two variables x and y, also called a linear system, consists of two equations that can be written in the following form: Ax + By = CandDx + Ey = F MM3A5c - Represent and solve realistic problems using systems of linear equations

Solution of a System  A solution of a system of linear equations in two variables is an ordered pair (x,y) that satisfies each equation. MM3A5c - Represent and solve realistic problems using systems of linear equations

Classifying a system of two linear equations  A system that has at least one solution is consistent.  If a system has no solution, the system is inconsistent. The graph of this system is a pair of parallel lines.  A consistent system that has exactly one solution is independent.  A consistent system that has infinitely many solutions is dependent. The graph of this system is a pair of lines that coincide (Cross). MM3A5c - Represent and solve realistic problems using systems of linear equations

How can you graph a system of linear equations?  Set up in Slope Intercept form  y= mx + b  What is your Slope and y-intercept?  Slope = Rise/Run  Where to start on the y-axis  GRAPH!  Where do they intersect?  That is the solution MM3A5c - Represent and solve realistic problems using systems of linear equations

 Ex.  Graph the linear system and estimate the solution. Then check the solution algebraically. y + 3x = 5Equation 1 y -2x = -5Equation 2 *From the graph, the lines appear to intersect at ( _, _ ). The solution can be checked algebraically. MM3A5c - Represent and solve realistic problems using systems of linear equations

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Put it all together…  Write and use a linear system.  Write what you know  Set up Equations  Graph the Equations  Answer in terms MM3A5c - Represent and solve realistic problems using systems of linear equations

 Ex.  Resort A charges \$70 per night, plus a one-time surcharge of \$5, Resort B charges \$65 per night, plus a one-time surcharge of \$20. after how many nights will the total cost of the two options be the same?  Determine the equations  Graph  MM3A5c - Represent and solve realistic problems using systems of linear equations

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Problems..  Page 8: 1-19  Show work  Circle answers  Graph paper will be provided MM3A5c - Represent and solve realistic problems using systems of linear equations

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