Systems Of Linear Equations


Linear equation can be defined as an equation which makes a straight line when it is plotted on a graph. Generally linear equation is written in form y = mx + b, Here ‘m’ represents the slope of line and ‘c’ denotes Y- intercept where line crosses y- axis. Here we will see system of linear equations. System of equation is a set or collection of different equations. Now we will understand process of solving systems of linear equations. Steps to be followed while solving System of Linear Equations are shown below.

Step 1: To solve system of linear equation first we take two equations. Suppose we have linear equations 2s + t = 12 and 4s – 3t = 6, now we will discuss how to solve system of linear equation.

Step 2: Then find value of one variable from one equation and then put that value in second equation. So from first equation we can easily find the value of ‘t’. So we can write first equation as:

⇒ 2s + t = 12, on further solving we can write it as:

⇒ t = 12 – 2s, we can find the value of ‘t’. Now put the value of ‘t’ in second equation. On putting value of ‘t’ in equation we get:

⇒ 4s – 3t = 6; put value of ‘t’ to find the value of ‘s’.

⇒ 4s – 3 * (12 – 2s) = 6, on further solving we get:

⇒ 4s – 36 + 6s = 6;

Now add like terms if present in equation;

⇒ 10s = 42;

⇒ s = 4.2

Now put the value of ‘s’ in 1 st equation.

⇒ t = 12 – 2s;

⇒ t = 12 – 2 * 4.2;

⇒ t = 3.6;

So value of ‘s’ and ‘t’ is 4.2 and 3.6,on plotting these values we get a straight line graph. This is all about linear equation system. Linear system of equations can contain more than two equations. 

Topics Covered in Systems Of Linear Equations

The Graphing Method

Graphing method is a diagrammatic representation of relationship between two or more than two variables. Graphs can be of various kinds such as line chart, plot chart, pie chart, column chart etc. Graphical representation may be on a Cartesian plane and is known as curve sketching. Various functions and equations can be explained using graphing methods.

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The Substitution Method

Substitution Method is a very simple method to solve one of the equations which contain unknown variables.

We solve for unknown variable and substitute it in other equation for calculating value of its variables. This is a accurate method. System of linear equations can be solved by use of the substitution method algebra.

Main use of substituti...Read More

The Addition (Elimination) Method

When we have two equations which has two unknown variables then for finding value of these unknown variables a method is used which is known as addition method. Addition Method is also called elimination method since here unknown variables are found by elimination method. In addition method algebra, two equations with two unknown variables are ...Read More

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