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An equation between two variables that gives a straight line when plotted on a graph.
‘Topics include analytic solutions of linear equations, equilibria, linearization, stability, phase portraits, bifurcations, simulations, and modeling methodology.’
‘The estimators are thus computed solving the linear equations obtained deriving equation for the unknowns.’
‘The resulting equation yields beta scores, which are multiplied by the independent variables once the linear equation is calculated.’
‘In this way of specifying coordinates a point has a linear equation, namely that of all lines through the point while a line has a pair of numbers namely the x and y coordinates of where it cuts the axes.’
‘They can solve a variety of two-step problems using variables, identify equivalent algebraic expressions, and solve linear equations and inequalities.’
‘Non-linear equations or linear equations with time delays are required for the system to exhibit of ‘limit cycle’ behavior.’
‘This relates to the way you graph linear equations by hand.’
‘With these assumptions, we can write the revenue management problem as a series of linear equations.’
‘Essentially linear equations are solved by making two guesses at the solution, then computing the correct answer from the two errors.’
‘Again a table would have been looked up to solve the linear equation ax = b.’
‘The above multiple linear equations, did not yield any co-linearity between the independent variables X 2 and X 5.’
‘There is, however, work in progress concerning the numerical solution of linear equations with several unknowns using electrical circuits.’
‘He worked on numerical methods for solving systems of linear equations and eigenvalue problems.’
‘These are called linear equations where A and B are, in general, any real numbers.’
‘Thymaridas also gave methods for solving simultaneous linear equations which became known as the ‘flower of Thymaridas’.’
‘Systems of linear equations were studied in the context of solving number problems.’
‘This is a word problem whose solution includes solving a system of two linear equations.’
‘Von Koch's first results were on infinitely many linear equations in infinitely many unknowns.’
‘Euler's theorem is far from the whole story for face vectors of polytopes, but it is not difficult to show that it is the whole story of linear equations on face numbers.’
‘Linear functions of the input and key make poor choices for encryption functions because such systems can always be broken by solving small sets of linear equations.’