LESSON 3 : SOLVING SYSTEMS USING THE GRAPHICAL METHOD
Systems of Equations – some general
linear system of 2 equations in 2 unknowns will have the following form:
solution of such a system of equations has two interpretations :
Geometric - the point of
intersection of the two straight lines.
Algebraic - the
ordered pair (x,y) of real numbers that satisfies both equations
at the same time.
of equations may be classified in the following way.
there are no points of intersection.
there is no solution to the system when solved.
the two lines are parallel.
is a unique solution.
lines intersect at a single point.
system is consistent and independent.
equations yield the same line
are an infinite number of solutions.
lines intersect at every point.
system is consistent and dependent.
Inconsistent systems have no
Consistent systems have either a unique solution or an infinite
number of solutions.
Methods of Solving Systems
The Graphical Method: