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Two equations or two systems of equations are equivalent, if they have the same set of solutions. The following operations transform an equation or a system of equations into an equivalent one – provided that the operations are meaningful for the expressions they are applied to: Adding or subtracting the same quantity to both sides of an ...
Equivalent equation: = + where y is the father's age ... To solve a linear equation with two variables (unknowns), requires two related equations. For example, if it ...
The term "Maxwell's equations" is often also used for equivalent alternative formulations. Versions of Maxwell's equations based on the electric and magnetic scalar potentials are preferred for explicitly solving the equations as a boundary value problem, analytical mechanics, or for use in quantum mechanics.
In the example, calculating the equivalent voltage: = + (+) + = + (+) + = = (Notice that R 1 is not taken into consideration, as above calculations are done in an open-circuit condition between A and B, therefore no current flows through this part, which means there is no current through R 1 and therefore no voltage drop along this part.)
For example, the set of all solution pairs (,) of the equation + = forms the unit circle in analytic geometry; therefore, this equation is called the equation of the unit circle. [ 21 ] In mathematical logic and computer science , an equation may described as a binary formula or Boolean -valued expression , which may be true for some values of ...
If the differential equations are equivalent in form, the dynamics of the systems they describe will be related. The example hydraulic equations approximately describe the relationship between a constant, laminar flow in a cylindrical pipe and the difference in pressure at each end, as long as the flow is not analyzed near the ends of the pipe.
For example, is an expression, while the inequality is a formula. To evaluate an expression means to find a numerical value equivalent to the expression. [ 3 ] [ 4 ] Expressions can be evaluated or simplified by replacing operations that appear in them with their result.
One of the main uses of the principle of permanence is to show that a functional equation that holds for the real numbers also holds for the complex numbers. [9] As an example, the equation + = hold for all real numbers s, t. By the principle of permanence for functions of two variables, this suggests that it holds for all complex numbers as well.