Download presentation

Presentation is loading. Please wait.

Published byEunice Harmon Modified over 7 years ago

1
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?

2
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

3
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

4
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

5
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

6
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

7
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

8
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

9
Page 6: 1-3 MM3A5c - Represent and solve realistic problems using systems of linear equations

10
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

11
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

12
Page 7: 4-7 MM3A5c - Represent and solve realistic problems using systems of linear equations

13
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

Similar presentations

© 2023 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google