Pair of Linear equation in two variables|| part 4|| Class 10|| Chapter 3
Good morning to all I am Prashant Jain, going to teach you about A Pair of linear equations in two variables.
Today, in part 4, we will learn Algebraic methods, specially Substitution Method and some word problems related to Class X NCERT Exercise 3.3
So all of my near and dear ones Lets learn…
In the previous section, we discussed how to solve a pair of linear equations graphically. The graphical method is not convenient in cases when the point representing the solution of the linear equations has non-integral coordinates like (√3,2√7), (–1.75,3.3), (4/13,1/19) etc. There is every possibility of making mistakes while reading such coordinates. Is there any alternative method of finding the solution? There are several algebraic methods, which we shall now discuss.
To understand the substitution method more clearly, let us consider it stepwise:
Step 1 : Find the value of one variable, say y in terms of the other variable, i.e., x from
either equation, whichever is convenient.
Step 2 : Substitute this value of y in the other equation, and reduce it to an equation in
one variable, i.e., in terms of x, which can be solved. Sometimes, as in Examples 9 and
10 below, you can get statements with no variable. If this statement is true, you can
conclude that the pair of linear equations has infinitely many solutions. If the statement
is false, then the pair of linear equations is inconsistent.
Step 3 : Substitute the value of x (or y) obtained in Step 2 in the equation used in
Step 1 to obtain the value of the other variable