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. 

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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 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:

• Substitution Method
• Elimination Method
• Graphical Method

Do you have any questions regarding the System of Linear Equations? You can ask here in the comment section below.

A linear equation represents a straight line on a graph. If two linear equations whose straight lines intersect each other at a point, they are called system of linear equations. The point of intersection is the common solution to those linear equations, and hence is the solution of system of linear equations.

Among the various methods to solve simultaneous equations, the Elimination Method is one of the most popular and easiest methods to solve the pair of simultaneous equations in two variables x and y.

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In this method, one variable either x or y is eliminated to find the value of another variable. And, for that, we need to make coefficients of any one variable equal by multiplying or dividing the equations by the least number so that the coefficients of x or y become equal in both the new equations. 

Then, by adding or subtracting according to these equal coefficients have opposite or same sign respectively, we get an equation which will have only one variable. Then, simplification will give the value of that variable.

 

After solving the value of either x or y obtained from the above steps is substituted in any one of the given equations to get the value of the other variable.