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Q: What are the different ways of graphing linear equations in two variables?

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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.

There can be linear equations with 1, 2, ... variables. Each of these is different since an equation with n variables belongs to n-dimensional space.

They are the same.

They are the simplest form of relationship between two variables. Non-linear equations are often converted - by transforming variables - to linear equations.

It means that there is no set of values for the variables such that all the linear equations are simultaneously true.

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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.

There can be linear equations with 1, 2, ... variables. Each of these is different since an equation with n variables belongs to n-dimensional space.

They are the same.

They are the simplest form of relationship between two variables. Non-linear equations are often converted - by transforming variables - to linear equations.

A system of linear equations is two or more simultaneous linear equations. In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.

The advantage of solving a system of linear equations by graphing is that it is relatively easy to do and requires very little algebra. The main disadvantage is that your answer will be approximate due to having to read the answer from a graph. Where the solution are integer values, this might be alright, but if you are looking for an accurate decimal answer, this might not be able to be achieved. Another disadvantage to solving linear equations by graphing is that at most you can have two unknown variables (assuming that you are drawing the graph by hand).

A system of linear equations.

a system of equations

Simultaneous equations have at least two unknown variables.

The solution of a system of linear equations is a pair of values that make both of the equations true.

It means that there is no set of values for the variables such that all the linear equations are simultaneously true.

simultaneous equations