3.3    algebraic methods of solving a pair of linear equations

    There are four methods for solving a pair of linear equations
    (i) Substitution method    
    (ii) Elimination method    
    (iii) Cross-multiplication method
    (iv) Graphical Method

3.3.2     Elimination Method
    Step–I:         Obtain the two equations
    Step–II:     First multiply both the equations by some suitable non-zero constant to make the coefficient of one variable (either x or y) numerically equal.
    Step–III:     Add or subtract one equation from the other, then one variable gets eliminated.
    Step–IV:     Solve the equation in one variable. 
    Step–V:     Substitute the value of x (or y) in any one of the given equations and find the value of another variable.

3.3.4     Graphical Method:
    In graphical method, we draw the graph of both equations using same pair of horizontal and vertical lines called X-axis and Y-axis respectively. Coordinates of the point(s) of intersection of the two lines is/are the solution.
    Nature of solutions:
    When we try of solve a pair of equations we could arrive at three possible results. They are, having
    (a) a unique solution
    (b) an infinite number of solutions
    (c) no solution