# Where the coefficients and solutions are integers the

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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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