where the coefficients and solutions are
integers
. The techniques
used are different and come from
number theory
. These equations are difficult in general; one
often searches just to find the existence or absence of a solution, and, if they exist, to count the
number of solutions.
Differential equations
are equations that involve one or more functions and their derivatives.
They are
solved
by finding an expression for the function that does not involve derivatives.
Differential equations are used to model processes that involve the rates of change of the
variable, and are used in areas such as physics, chemistry, biology, and economics.
The "
=
" symbol, which appears in every equation, was invented in 1557 by
Robert Recorde
, who
considered that nothing could be more equal than parallel straight lines with the same length.
[3]
Example of Equation

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The following are some examples of equation.
10 + 2 = 12
4a - 3b = 1
e
x
+ y = - 2
4 + 6 = 10
12
=
7
+
5
An inequality says that two values are not equal.
a ≠ b
says that a is not equal to b
There are other special symbols that show in
what way
things are not equal.
a < b
says that a is less than b
a > b
says that a is greater than b
(those two are known as strict inequality)
a ≤ b
means that a is less than or equal to b
a ≥ b
means that a is greater than or equal to b.
Two Graphs of linear equations in two variables
In
mathematics
, a
linear equation
is an
equation
that may be put in the form
where are the
variables
(or
unknowns
or
indeterminates
), and are the
coefficients
, which are
often
real numbers
. The coefficients may be considered as
parameters
of the equation, and may

be stated as arbitrary
expressions
, restricted to not contain any of the variables. To yield a
meaningful equation for non-zero values of the coefficients are required not to be all zeros.
In the words of algebra, a linear equation is obtained by equating to zero a
linear
polynomial
over some
field
, where the coefficients are taken from, and that does not contain the
symbols for the indeterminates.
The
solutions
of such an equation are the values that, when substituted to the unknowns, make
the equality true.
The case of just one variable is of particular importance, and it is frequent that the term
linear
equation
refers implicitly to this particular case, in which the name
unknown
for the variable is
sensibly used.
All the pairs of numbers that are solutions of a linear equation in two variables form a
line
in
the
Euclidean plane
, and every line may be defined as the solutions of a linear equation. This is
the origin of the term
linear
for qualifying this type of equations. More generally, the solutions of

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- Fall '19