# What is a System of Linear Equations

A System of Linear Equations is a pair of linear equations having a unique solution. To understand the system of linear equations let’s take an example related to our daily life.

The total cost of 2 kg sugar and 1 kg tea is Rs. 180 while the total cost of 1 kg sugar and 2 kg tea is Rs. 240. Find the rate of each per kg.

Here, we need to find the cost of 1 kg sugar as well as the cost of 1 kg tea.

Let the cost of 1 kg sugar be Rs. x
and cost of 1 kg tea be Rs. y

The cost of 2 kg sugar and 1 kg tea = Rs. 180
Therefore, 2x + y = 180 …………….(i)

Also, the cost of 1 kg sugar and 2 kg tea = Rs. 240
Therefore, x + 2y = 240 …………….(ii)

Here, x and y are two variables in each of a pair of above linear equations. If we show them in a graph, each equation gives a straight line and they intersect with each other at a unique point which gives the values of x and y satisfying both the equations. Such a pair of linear equations which satisfied by a unique solution is called a system of linear equations.

There are 3 different methods for solving a system of linear equations:

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