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  2. System of linear equations - Wikipedia

    en.wikipedia.org/wiki/System_of_linear_equations

    The solution set for the equations xy = −1 and 3x + y = 9 is the single point (2, 3). A solution of a linear system is an assignment of values to the variables ,, …, such that each of the equations is satisfied. The set of all possible solutions is called the solution set. [5]

  3. Equation solving - Wikipedia

    en.wikipedia.org/wiki/Equation_solving

    One particular solution is x = 0, y = 0, z = 0. Two other solutions are x = 3, y = 6, z = 1, and x = 8, y = 9, z = 2. There is a unique plane in three-dimensional space which passes through the three points with these coordinates, and this plane is the set of all points whose coordinates are solutions of the equation.

  4. Linear equation - Wikipedia

    en.wikipedia.org/wiki/Linear_equation

    Vertical line of equation x = a Horizontal line of equation y = b. Each solution (x, y) of a linear equation + + = may be viewed as the Cartesian coordinates of a point in the Euclidean plane. With this interpretation, all solutions of the equation form a line, provided that a and b are not both zero. Conversely, every line is the set of all ...

  5. Polynomial - Wikipedia

    en.wikipedia.org/wiki/Polynomial

    In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms.

  6. Annihilator method - Wikipedia

    en.wikipedia.org/wiki/Annihilator_method

    In mathematics, the annihilator method is a procedure used to find a particular solution to certain types of non-homogeneous ordinary differential equations (ODEs). [1] It is similar to the method of undetermined coefficients, but instead of guessing the particular solution in the method of undetermined coefficients, the particular solution is determined systematically in this technique.

  7. How to Solve It - Wikipedia

    en.wikipedia.org/wiki/How_to_Solve_It

    Pólya mentions that there are many reasonable ways to solve problems. [3] The skill at choosing an appropriate strategy is best learned by solving many problems. You will find choosing a strategy increasingly easy. A partial list of strategies is included: Guess and check [9] Make an orderly list [10] Eliminate possibilities [11] Use symmetry [12]

  8. Characteristic equation (calculus) - Wikipedia

    en.wikipedia.org/wiki/Characteristic_equation...

    Similarly, if c 1 = ⁠ 1 / 2i ⁠ and c 2 = − ⁠ 1 / 2i ⁠, then the independent solution formed is y 2 (x) = e ax sin bx. Thus by the superposition principle for linear homogeneous differential equations , a second-order differential equation having complex roots r = a ± bi will result in the following general solution:

  9. Separation of variables - Wikipedia

    en.wikipedia.org/wiki/Separation_of_variables

    Separation of variables may be possible in some coordinate systems but not others, [2] and which coordinate systems allow for separation depends on the symmetry properties of the equation. [3] Below is an outline of an argument demonstrating the applicability of the method to certain linear equations, although the precise method may differ in ...