May 2009

2x2 systems of linear equations

GRADE: NOVENA

AREA: Matemáticas

TOPIC: SYSTEMS OF LINEAR EQUATIONS

PREPARED BY: ADRIANA HINCAPIE

hincapié.adriana @ gmail.com

VILLAVICENCIO. META. COLOMBIA

KEYWORDS: equations, linear systems, 2x2, problems, methods, replacing , reduction, equalization, graphic.

ACHIEVEMENTS:

Identifies, represents and solve linear equations .

poses and solves problems with equations.

ago appropriate use of information technologies and communication.

generating Question: How do I apply the solution of linear equations in daily life?

LEARNING SITUATION

Every day you will find that many of the situations that revolve around you may arise through an equation, eg

In my class is 35 students. We have given our strong performance by each girl 2 pens and a notebook for each child. If in total have been 55 gifts, how many boys and girls are in my class?

an equation how would this situation?

What is the solution to the problem question?

I invite you to read the following information to learn to raise and develop linear equations.

Read carefully:

system of linear equations

All

equality of the form ax + by = c where a, b, c Є R is a linear equation with two unknowns.

Each couple ordered real numbers that satisfies this equation is a solution of it.

For example, to find solutions to the equation y - 3x = 2, and cleared, and then assign arbitrary values \u200b\u200bto x.

In this way, giving values \u200b\u200bax, You can get infinite values \u200b\u200bfor y. Thus it is said that the linear equation y - 3x = 2 is an equation undetermined.

Any linear equation with two unknowns is an indeterminate equation.

A set of two or more unknowns is called linear systems of equations or systems of simultaneous equations.

For example, the set

3x - y = 7

2x + y = 8

is a 2x2 system, it is composed of two equations with two unknowns. solution of this system is the pair (3.2) since it satisfies the two equations simultaneously.

The set

3x - 2y + 3z = 16

x + 3y - 6z = -23

5x + 4y - 2z = -9

is a 3x3 system, it is composed of three equations with three unknowns. solution of this system is given by the triplet (1, -2, 3)