Simultaneous equations by Elimination Method

Steps for solve linear equations with elimination method.

Step 1: First we arrange both equations in standard form, placing like variables and constants one above the other.

Step 2: Choose a variable (x or y) to eliminate, Multiply both equations by a suitable(non zero) constant to make the coefficients of one variable (x or y) to be equal.

Step 3: Add or subtract one equation, from other. 

a. The terms having the same coefficient but opposite in signs then add them.

b. The terms having the same coefficient but different in signs then subtract them.

Step 4: Now equations remains in one variable(x or y) because one variable is eliminated.

Step 5: Solve the remaining equation, in one variable (x or y) so, obtained the value of one variable(x or y).

Step 6: Substitute this value of (x or y) in either of the original equations to get the value of the other number. 

Example 1:  Solve equation by elimination method.  

                        x + y = 12
                            x – y = 4 

We can eliminate the y variable, by addition of two equations.

                            x + y = 12

                            x – y = 4 
                        ____________
                                2x = 16

                                  x = 16/2
                                  x = 8

The value of x, can now substituted into either of the original equations to find the value of y,

                              x + y = 12

                              8 + y = 12

                                    y = 12 – 8

                                    y = 4

           The solution of linear equation is (8, 4)

Example: 2

                             2x + y = 5
                                3x + 2y = 8

multiply the first equation by 3, and second equation by 2, so that the coefficients of x are same 

                                6x + 3y = 15

                                6x + 4y = 16

The coefficients of both equations are same and sign is also same so that subtract equation 2 from equation 1,

                                6x + 3y = 15

                                6x + 4y = 16
                               –     –         –
                             ______________
                                        -y = -1
                                          y = 1

The value of y, can now substituted into either of the original equations to find the value x,

                               6x + 3y = 15

                               6x + 3x(1) = 15

                               6x + 3 = 15

                                     6x  = 15 – 3

                                     6x = 12

                                     x = 12/6

                                     x = 2

        The solution of linear equation is (2, 1)