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Coordinates,Distance and Midpoint

Linear Inequalities

The Graphical Method

Substitution & Elimination

Solving Systems Using Matrices

Problem Solving

Systems of Inequalities

Systems with 3 Equations in 3 Unknowns

Review&Test

UNIT 2 : SYSTEMS OF EQUATIONS

LESSON 3 : SOLVING SYSTEMS USING THE GRAPHICAL METHOD

 

Systems of Equations some general considerations

 

A linear system of 2 equations in 2 unknowns will have the following form:

 

 

The solution of such a system of equations has two interpretations :

 

i)               Geometric - the point of intersection of the two straight lines. Or

ii)             Algebraic - the ordered pair (x,y) of real numbers that satisfies both equations

at the same time.

 

Systems of equations may be classified in the following way.

 

Inconsistent Systems:

 

-          there are no points of intersection.

-          there is no solution to the system when solved.

-          the two lines are parallel.

 

 

Consistent Systems:

a)      there is a unique solution.

the lines intersect at a single point.

the system is consistent and independent.

 

 

 

b)      both equations yield the same line

there are an infinite number of solutions.

the lines intersect at every point.

the system is consistent and dependent.

 

 

 

Summary

 

Inconsistent systems have no solution.

 

Consistent systems have either a unique solution or an infinite number of solutions.

 

 

Methods of Solving Systems

 

The Graphical Method:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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