SYSTEMS OF EQUATIONS WITH 2 VARIABLES
(1) A
system of equations
is a collection of equations with the same set of variables. A
system of linear equations will only have linear equations in it (i.e. equations of the
form
Ax
+
By
+
Cz
+
....
= 0 where
x,y,z,
etc. represent the variables and
A,B,C,
etc.
represent the coeﬃcients of the variables).
(2) A
solution
to the system of equations will be the set of values that makes
all
the
equations in the system true when you plug them in. In a 2dimensional linear system,
we call the solution an
ordered pair
(
x,y
), because the order matters (i.e. (
x,y
)
6
= (
y,x
)
unless
x
=
y
).
(3) Graphically, the solution to a system of equations with 2 variables is the point(s) where
the lines intersect on the xyplane. If the lines do not intersect at any point, then there
is no solution to the system.
(4) A system of equations with 2 variables is generally of the form:
(
Ax
+
By
=
C
Dx
+
Ey
=
F
(5) When we encounter a system with 2 variables, we should solve the system using
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 Fall '10
 Beaulieu
 Linear Equations, Systems Of Equations, Equations, Probability, Expression, Elementary algebra

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