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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?

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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

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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

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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

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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

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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

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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

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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

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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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