Chapter 2.1: Systems of Linear Equations
•
A
linear
equation is an equation in which each variable has
degree one.
•
We call them linear because when a linear equation involves
only two variables, the equation describes a straight line.
Examples:
Here are some examples of linear equations.
7
y
+ 3
x
= 2
x
+
y
+
z
= 7
7
a

11
17
b
+
72
3
c
= 91
Here are some examples of nonlinear equations.
x
2
+ 5
x
= 2
x

yz

√
w
= 7
a
3

b
3
2
= 2
•
A
system of linear equations
is a collection of one or more
linear equations.
•
A
solution
of a system is a set of values which satisfies
all
of
the equations in the system.
Example:
Verify that
x
= 1 and
y
= 2 form a solution for the
following system.
2
x
+ 5
y
= 12
2
x
+ 6
y
= 14
We will look at the first equation, at the right and left sides
separately, substituting in the given values for
x
and
y
.
L.S.
= 2(1) + 5(2)
= 2 + 10
= 12
1
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R.S.
= 12
Since the left side is equal to the right side for the values
x
=
1
,y
= 2, then we say that these values
satisfy
the first equation.
We do the same for the second equation.
L.S.
= 2(1) + 6(2)
= 2 + 12
= 14
R.S.
= 14
The values also satisfy the second equation.
Since the values
x
= 1
,y
= 2 satisfy all of the equations in the system, then these
values are a solution of the system.
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 Spring '11
 stephenlang
 Calculus, Linear Equations, Equations, Systems Of Linear Equations, Quadratic equation, Elementary algebra, Quintic equation

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