- Books Name
- Rakhiedu Mathematics Book

- Publication
- Param Publication

- Course
- CBSE Class 10

- Subject
- Mathmatics

** 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