Are there differencesbetween independentand dependent variablesin
mathematics and statistics?
Yes, there are subtle differences between these two types of variables in mathematics and
statistics. In mathematics, independent variables are those whose value determines the
value of other variables; in statistics, they are a manipulated variable in an experiment or
study whose presence or degree determines the change in the dependent variable.
Dependent variables in mathematics are those variables whose value is deter-
mined by an independent variable; in statistics, they are the observed variables in an
experiment or study whose changes are determined by the presence or degree of one
or more independent variables. (For more information about variables in statistics,
see “Applied Mathematics.”)What is a solution?
When an equation has a variable, the number that replaces the unknown and makes the
equation true is called a solution. For example, for the equation (5 y) 2 12, ywould
be 2, or “2” is the solution that makes the equation true. To work this out, the process
would look like this: (5 2) 2 12; 10 2 12; and, finally, 12 12. Remember,
when finding a solution for an equation, one must follow any parentheses, exponents,
multiplications, divisions, additions, and subtractions in the correct order of operation.How do you simplifyan algebraic equation?
The best way to simplifyan equation is to combine like terms, which makes the equa-
tion simpler to solve. Numbers may be combined, as well as any terms with the same
136 variable.
How did symbols for unknowns and knowns
in algebraic equations develop?I
n 1591, François Viète was the first to write and solve general algebraic equa-
tions by introducing the systematic use of letters as algebraic symbols. He
used vowels (a, e, i, o, u) for the unknowns and consonants (the rest of the
alphabet) for the coefficients (or knowns).But it was René Descartes who introduced a new way of using letters in the
alphabet in his work La Gèometrie. He used the letters at the end of the alphabet
(x, y, ...) for unknowns and the beginning of the alphabet (a, b, ...) for knowns
(in many instances, these letters are italicized). This standard is still used in
algebra today.