About System of equations
Jul 09, 2014 240 likes | 617 Views Solving Systems of Equations. Vocabulary. System of Equations: a set of equations with the same unknowns Consistent : a system of equations with at least one ordered pair that satisfies both equations. Download Presentation Solving Systems of Equations An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher. Presentation Transcript Solving Systems of EquationsVocabulary • System of Equations: a set of equations with the same unknowns • Consistent: a system of equations with at least one ordered pair that satisfies both equations. • Dependent: a system of equations that has an infinite number of solutions; (lines are the same) • Inconsistent: a system of equations with no solution • Independent: a system of equations with exactly one solution • Solution to a system of equations: a point that makes both equations trueDifferent Methods for Solving Systems • Elimination Method: adding or subtracting the equations in the systems together so that one of the variables is eliminated; multiplication might be necessary first • Substitution Method: Solving one of a pair of equations for one of the variables and substituting that into the other equation • Graphing Method: Solving a system by graphing equations on the same coordinate plane and finding the point of intersection.Substitution Method STEPS: • Solve one of the equations for one of the variables • Substitute, or replace, the resulting expression into the other equation for the solved variable • Solve the equation for the second variable • Substitute the found variable into either
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- System of linear equations - Wikipedia
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The Numpy library can be used to perform a variety of mathematical/scientific operations such as matrix cross and dot products, finding sine and cosine values, Fourier transform and shape manipulation, etc. The word Numpy is short-hand notation for "Numerical Python".In this article, you will see how to solve a system of linear equations using Python's Numpy library.What is a System of Linear Equations?Wikipedia defines a system of linear equations as:In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same set of variables.The ultimate goal of solving a system of linear equations is to find the values of the unknown variables. Here is an example of a system of linear equations with two unknown variables, x and y:Equation 1:4x + 3y = 20-5x + 9y = 26To solve the above system of linear equations, we need to find the values of the x and y variables. There are multiple ways to solve such a system, such as Elimination of Variables, Cramer's Rule, Row Reduction Technique, and the Matrix Solution. In this article we will cover the matrix solution.In the matrix solution, the system of linear equations to be solved is represented in the form of matrix AX = B. For instance, we can represent Equation 1 in the form of a matrix as follows:A = [[ 4 3] [-5 9]]X = [[x] [y]]B = [[20] [26]]To find the value of x and y variables in Equation 1, we need to find the values in the matrix X. To do so, we can take the dot product of the inverse of matrix A, and the matrix B as shown below:X = inverse(A).BIf you are not familiar with how to find the inverse of a matrix, take a look at this
