unit 1.2 – solve linear systems by graphing mm3a5c - represent and solve realistic problems using...
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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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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
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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 = C and Dx + 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 = 5 Equation 1y -2x = -5 Equation 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..
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MM3A5c - Represent and solve realistic problems using systems of linear equations