Algebra II 10-23-13 day 36 Chapter 3 Systems of Linear Equations.

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Presentation transcript:

Algebra II day 36 Chapter 3 Systems of Linear Equations

Use graphing to solve the following system of equations y=2-9x y=8-3x

Classifying Systems of Equations If a system has infinitely many solutions, it is called dependent. If a system does not have a solution, it is called inconsistent. If a system of equations has at least one solution, it is called consistent. If a system has exactly one solution, it is called independent.

ex. Solve the system for x and y by graphing x-2y=4 x+6=2y

Practice: p.161 # , 14, 17

ex. Solve the system for x and y by graphing -2x+3y=12 -6y= -24-4x

Algebraic Methods for Solving Systems of Equations 1. Substitution- Solve one equation for a variable and substitute into the other. y=2-9x y=8-3x

2x+y=3 3x-2y=8 Which variable is the easiest to solve for?

Use substitution to solve the following system of equations 18x+2y=4 3x+y=8

Homework: p.161 #27, 29, 31, 37 p.163 #59

Algebraic Methods for Solving Systems of Equations 1. Substitution- Solve one equation for a variable and substitute into the other. 2x+y=3 3x-2y=8 Which variable is the easiest to solve for?

Use substitution to solve the following system of equations y=2-9x y=8-3x

3.2 Solving Systems using Elimination Solve using elimination 2x + 5y = 15 -4x + 7y = -13

Use substitution to solve the following system of equations 18x+2y=4 3x+y=8

Try Solve using elimination 4x - 3y = 15 8x + 2y = -10

Solve using Elimination 2x + 5y = 12 -4x - 10y = -24

Solve using Elimination 2x + 5y = 15 -3x - 7.5y = -22.5

3.2 Solving Systems of Equations using Elimination The manager of a movie theater wants to know the number of adults and children who go to the movies. The theater charges $8 for each adult ticket and $4 for each child ticket. At a showing where 200 tickets were sold, the theater collected $1304. How many adults attended the showing? How many children?

3.1 Solving Systems of Equations using Graphing and Substitution The manager of a movie theater wants to know the number of adults and children who go to the movies. The theater charges $8 for each adult ticket and $4 for each child ticket. At a showing where 200 tickets were sold, the theater collected $1304. How many adults attended the showing? How many children?

Extra (If needed) Solve using elimination 6r + 7s = r + s = -6

3.2 Solving Systems using Elimination Solve using elimination 2x + 5y = 15 -4x + 7y = -13

Solve using Elimination 2x + 5y = 12 -4x - 10y = -24

Try Solve using elimination 4x - 3y = 15 8x + 2y = -10

Solve using Elimination 2x + 5y = 15 -3x - 7.5y = -22.5