Simultaneous Linear Equations II: Elimination Method – JSS3 Mathematics Lesson Note (Second Term)

 ELIMINATION METHOD

This method is very useful to solve simultaneous equations especially when none of the coefficients of the unknown is 1.

Example III.

Solve the following simultaneous equations by elimination method.

(a)    6x + 5y = 15 (1)                                        (b)    4c – 4d = 9

         3x + 5y = 12 (2)                                                    5c + 4d = 18

One of the unknown “Y” has an equal coefficient and with the same signs so we subtract the two equations to eliminate y terms.

6x + 5y – (3x + 5y) = 15 – 12

6x + 5y – 3x – 5y = 3

6x – 3x + 5y – 5y = 3

3x + 0 = 3

=x=1

 To find y, substitute x=1 in either (1) or (2) using equation

 (1) 6x + 5y = 15

6(i) + 5y = 15

6 + 5y = 15

5y = 15 – 6 = y=

(b)    4c – 4d = 9              (1)

         5c + 4d = 18            (2)

One of the unknown “d” has an equal coefficient but with a different sign so we add the two equations to eliminate “d”

4c – 4d + 5c + 4d = 9 + 18

4c + 5c – 4d + 4d = 27

  =  

C = 3

To find d substitute c = 3 into (1)

4c – 4d = 9

4(3) – 4d = 9

4d = 12 – 9 =  D =

WRAP-UP AND ASSESSMENT

In the elimination method, you may need to multiply one or both of the equations by a number to obtain a variable with the same coefficient in both equations.  Then add both equations when the signs of the variables you want to eliminate are opposite but subtract them when the signs are the same.

Exercise: 16 4 No 2, 3, 7 – 11.

Use the elimination method to solve the following simultaneous equations.

2.     6x + 7y = 15                                                 3)                 4x + 3y = 10

         6x – 9y = 31                                                                         4x + 5y = 8

7)     2x + 3y = 8                                                   8)                 3x + 4y = 10

         3x + 2y = 7                                                                           2x + 5y = 9

9)     4x + 3y = 11                                                 10)               4a + 3b = 3

         3x – 4y = 2                                                                           3a + 2b = 1

TICKET OUT

Solve the following Simultaneous equation by Elimination method. Exercise 16.4 No 12 -1