Question

Define substitution,elimination,cross multiplication methods and give an example for each

Answer 1

Step-by-step explanation:

ALGEBRAIC METHOD OF SOLVING A PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

Some times, graphical method does not give an accurate answer. While reading the co-ordinate of a point on a graph paper we are likely to make an error. So we require some precise method to obtain accurate result. The algebraic methods are given below :

(i) Method of elimination by substitution.

(ii) Method of elimination by equating the coefficients.

(iii) Method of cross multiplication.

ALGEBRAIC SOLUTION BY SUBSTITUTION METHOD

To solve a pair of linear equations in two variables x and y by substitution method, we follow the following steps:

Step-I : Write the given equations

a1x + b1y + c1 = 0 ...(i)

and a2x + b2y + c2 = 0 ...(ii)

Step-II : Choose one of the two equations and express y in terms of x (or x in terms of y), i.e., express, one variable in terms of the other.

Step-III : Substitute this value of y obtained in step-II, in the other equation to get a linear equation in x.

Step-IV : Solve the linear equation obtained in step-III and get the value of x.

Step-V : Substitute this value of x in the relation obtained in step-II and find the value of y.