Question 248596
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Linear equations are of degree 1.  The degree of an equation is the largest SUM of the exponents on any term.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ y\ = 5]


is linear because an equivalent form is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^1\ +\ y^1\ =\ 5]


And the largest exponent is 1, hence the degree of the equation is 1.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ xy\ =\ 3]


is NOT linear.  Look at the equivalent form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^1y^1\ =\ 3]


The degree of a term is the SUM of the exponents in that term, hence the *[tex \LARGE xy] term is of degree 2, therefore the equation is of degree 2, and therefore not linear.


Note that *[tex \LARGE x\ =\ \frac{3}{y}] is equivalent to the above non-linear equation and is also non-linear.


Obviously, any equation that has higher powers is also non-linear.  Included in the non-linear category are exponential, logarithmic, and 


The standard form of a two-variable linear equation is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ Ax\ +\ By\ = C]


Some texts require that A, B, and C be integers for proper standard form.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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