Contents

Introduction

Elimination Method

Substitution Method

Linear and non-linear equations 

Problem Solving

Quiz 

Algebra Main Page

Substitution Method

Example 1:

Solve the simultaneous equations

7x - 2y = 21, 4x + y = 57

  7x - 2y = 21 --------(1)

From (2): y = 57 - 4x --------(3)

 

Substitute (3) into (1): 7x - 2(57 - 4x) = 21

                                  7x - 114 + 8x = 21

                                                15x = 114 + 21

                                                      = 135

                                                    x = 9

 

Substitute x=9 into (3):  y = 57 - 4(9)

                                      = 57 - 36

                                      = 21

 

the solution set is x = 9, y = 21.

 

Example 2:

 

Solve the simultaneous equations

 

3x + 2y = 7, 9x + 8y = 22

 

   3x + 2y = 7  --------(1)

      9x + 8y = 22 --------(2)

From (1): 2y = 7 - 3x

                y =

The coefficients of y in both equations will be numerically equal if we multiply (1) by 2 and (2) by 3, since the LCM of 6 and 4 is 12.

 

(1) x 2:      26x - 12y = 40 --------(3)

(2) x 3:      21x +12y = 54 --------(4)

(3) + (4):           47x = 94

                            x = 2

 

Substitute x = 2 into (1):   13(2) - 6y = 20

                                                  6 = 6y

                                                  y = 1

 

  x = 2, y =1.