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.
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