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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: