Math Doubts

System of Linear equations

A collection of two or more linear equations that have same set of variables is called a system of linear equations.


The meaning of system is a set of connected things. In some cases, two or more linear equations have a connection and the relationship between them can be understood from their same set of variables.


$x+3y-5 = 0$ and $7x-8y-6 = 0$ are two linear equations.

system of linear equations

The two linear equations have a connection and it is they both have same set of variables $x$ and $y$. Therefore, a collection of such linear equations is called as system of linear equations and it is simply called as linear system.

When $x = 2$ and $y = 1$, the two linear equations are satisfied simultaneously.

  1. $2+3(1)-5 = 0$
  2. $7(2)-8(1)-6 = 0$

Therefore, the system of linear equations $x+3y-5 = 0$ and $7x-8y-6 = 0$ are called as simultaneous linear equations.

Methods of solving

The system of simultaneous linear equations can be solved in three different methods.

  1. Substitution method
  2. Elimination method
  3. Cross multiplication method
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