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Two equations both of which can be written in the form Ax + By = C are called a system of linear equations
or
a linear system
.
A solution to a system of linear equations
is an ordered pair that satisfies all equations in the system.
Ex.
(3, 1)
is a solution to the system
=
+
=

13
4
5
2
y
x
y
x
Since 2(3)5=1 is true and 4(3)+1=13 is true.
EX 1:
Determine whether each ordered pair is a solution of the system
=
+

=

4
2
4
3
2
y
x
y
x
a) (1, 2)
b) (7, 6)
Graphing
– not very exact unless using a graphing utility – will not be accepted as work for our problems!
Substitution
Steps
:
1.) Solve one of the equations for one of the variables.
2.) Substitute that into the other equation. (should now just have one variable left)
3.) Solve equation for that remaining variable.
4.) Substitute solution back in to either equation to solve for other variable.
5.) Check solution.
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 Fall '08
 Mcbride,V
 Linear Equations, Equations, Systems Of Linear Equations

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