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

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.



Vocabulary

Systems of two linear equations Solution of a System Consistent Inconsistent Independent Dependent

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


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.


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


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.


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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


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


Page 7: 4-7


Problems..

Page 8: 1-19 Show work Circle answers Graph paper will be provided


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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