143
L14
Systems of Equations
A
system of equations
is a set of two or more equations,
each containing one or more variables.
The
solution set
of a system of two equations in two
variables
is the set of all ordered pairs
(, )
x y
that satisfy
both equations. Geometrically, they are
points of
intersection
of the graphs of the equations.
Thus, the solution set
of the system of two equations in
two variables is the
set of all points of intersection
of
their graphs, if any.
If a system has at least one solution, it is called
consistent
; otherwise, it is called
inconsistent
.
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Systems of Linear Equations in Two Variables
A system of two linear equations in two variables
represents two lines.
There are three possibilities
:
1.
The lines
intersect at one point
– one solution;
the system is
consistent
and the equations are called
independent
.
2.
The lines are
coincident
– infinitely many solutions;
the system is
consistent
and the equations are called
dependent
.
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 Summer '08
 GERMAN
 Calculus, Systems Of Equations, Equations, Elementary algebra, 10%, 6%, 10 mL, 5.5%

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