Simultaneous Linear Equations

Simultaneous Linear Equations

Simultaneous linear equations are a pair of linear equations having a unique solution. To understand about  simultaneous linear equations let’s take an example related to our daily life.


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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 cost of 1 kg sugar as well as cost of 1 kg tea.

            Let 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 are called simultaneous linear equations.

There are 3 different methods of solving simultaneous linear equations:

i.        Substitution Method
ii.      Elimination Method
iii.     Graphical Method

You can comment your questions or queries regarding simultanious linear equations here.