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2. System of linear equations - Wikipedia

   en.wikipedia.org/wiki/System_of_linear_equations

   The solution set for the equations x − y = −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. Linear equation over a ring - Wikipedia

   en.wikipedia.org/wiki/Linear_equation_over_a_ring

   Let R be an effective commutative ring.. There is an algorithm for testing if an element a is a zero divisor: this amounts to solving the linear equation ax = 0.; There is an algorithm for testing if an element a is a unit, and if it is, computing its inverse: this amounts to solving the linear equation ax = 1.

4. Method of matched asymptotic expansions - Wikipedia

   en.wikipedia.org/wiki/Method_of_matched...

   In mathematics, the method of matched asymptotic expansions [1] is a common approach to finding an accurate approximation to the solution to an equation, or system of equations. It is particularly used when solving singularly perturbed differential equations. It involves finding several different approximate solutions, each of which is valid (i ...

5. Universal joint - Wikipedia

   en.wikipedia.org/wiki/Universal_joint

   The solution for is not unique since the arctangent function is multivalued, however it is required that the solution for be continuous over the angles of interest. For example, the following explicit solution using the atan2 ( y , x ) function will be valid for − π < γ 1 < π {\displaystyle -\pi <\gamma _{1}<\pi } :

6. System of differential equations - Wikipedia

   en.wikipedia.org/wiki/System_of_differential...

   For an arbitrary system of ODEs, a set of solutions (), …, are said to be linearly-independent if: + … + = is satisfied only for = … = =.A second-order differential equation ¨ = (,, ˙) may be converted into a system of first order linear differential equations by defining = ˙, which gives us the first-order system:

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