Gaussian elimination is used to solve systems of linear equations.
You would solve them in exactly the same way as you would solve linear equations with real coefficients. Whether you use substitution or elimination for pairs of equations, or matrix algebra for systems of equations depends on your requirements. But the methods remain the same.
Elimination and substitution are two methods.
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You cannot solve one linear equation in two variables. You need two equations that are independent.
Gaussian elimination is used to solve systems of linear equations.
You would solve them in exactly the same way as you would solve linear equations with real coefficients. Whether you use substitution or elimination for pairs of equations, or matrix algebra for systems of equations depends on your requirements. But the methods remain the same.
Elimination and substitution are two methods.
Linear Algebra is a branch of mathematics that enables you to solve many linear equations at the same time. For example, if you had 15 lines (linear equations) and wanted to know if there was a point where they all intersected, you would use Linear Algebra to solve that question. Linear Algebra uses matrices to solve these large systems of equations.
The answer depends on whether they are linear, non-linear, differential or other types of equations.
Solving linear systems means to solve linear equations and inequalities. Then to graph it and describing it by statical statements.
Elimination and substitution are two methods.
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You cannot solve one linear equation in two variables. You need two equations that are independent.
There is no simple answer. Sometimes, the nature of one of the equations lends itself to the substitution method but at other times, elimination is better. If they are non-linear equations, and there is an easy substitution then that is the best approach. With linear equations, using the inverse matrix is the fastest method.
I have never seen the term 'symbolic' used in this way. There are 4 methods used to solve a system of linear equations in two variables. Graphing, Substitution, Elimination, and Cramer's Rule.
Step-wise substitution of variablesStep-wise elimination of variablesGraphical[Generalised] Inversion of coefficient matrix