Lecture 19: Sections 7.1 and 7.2
System of Equations
Def.
A
system of equations
is a collection of
two or more equations, each containing one or more
variables.
A
solution
of a system of equations consists of
values of the variables that satisfy
eachequation
in
the system. To
Solve
a system is to find all solutions
of the system.
A system is
consistent
if it has at least one solution;
otherwise it is called
inconsistent
.
Def.
A system of the form
uni007B.alt04
u1D44E
1
u1D465
+
u1D44F
1
u1D466
=
u1D450
1
u1D44E
2
u1D465
+
u1D44F
2
u1D466
=
u1D450
2
is a
system of two linear equations in two
variables
.
The solution set of the system is all ordered pairs
(
u1D465,u1D466
) that satisfy the system.
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Solving by Graphing
ex.
Solve each system:
1)
uni007B.alt03
u1D465
+ 2
u1D466
= 4
u1D465
−
u1D466
= 1
2)
uni007B.alt03
u1D465
−
u1D466
=
−
1
−
2
u1D465
+ 2
u1D466
= 2
3)
uni007B.alt03
u1D465
+
u1D466
= 3
u1D465
+
u1D466
=
−
2
We have three possibilities:
1.
The lines intersect at one point.
The system is
consistent with exactly one solution. The equations
are
independent
.
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 Spring '08
 GERMAN
 Algebra, Trigonometry, Equations, Elementary algebra, $5, $6, Steve

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