Simultaneous Equations

 

 

 

Contents

 

Introduction

 

Elimination Method

 

Substitution Method

 

Linear and non-linear equations 

 

Problem Solving

 

Quiz 

 

 

Algebra Main Page

 

Solving Linear & Quadratic Equations

Example 1:

Solve the simultaneous equations

x + 2y = 1, x2 + y2 = 57

    x + 2y = 1 --------(1)

      x2 + y2 = 57 --------(2)
From (1): x= 1- 2y --------(3)    (make one of the variable the subject of the linear equation)
 
Substitute (3) into (2): (1-2y)2 + y2 = 10
                           1- 4y + 4y2 +y2  = 10
                                   5y2 - 4y -9 = 0
                               (5y - 9) (y +1)= 0
                                      y = 9/5 or -1
 
Substitute the values of y into the equation (3) to find the value of x.
 
when y = 9/5             x = 1 -2(9/5)=-13/5
when y = -1               x = 1 -2(-1) = 3
 
the solution set is x = , y = 9/5
                          or x = 3, y =-1

 
Example 2:
 
Solve the simultaneous equations
 
2x - y = 2, x2 +y2 = 8
 
         2x - y = 2  ---------(1)
            x2 + y2 = 8 --------(2)
From (1): y = 2x - 2 --------(3)
 
Substitute (3) into (2): x2 + (2x - 2)2 = 8
                       x2 + 4x2 - 8x + 4 - 8 = 0
                                    5x2 - 8x - 4 = 0
                                (5x + 2)(x - 2) = 0
                                      x=-2/5 or 2
 
 
when x = -2/5            y = 2(-2/5) - 2=
when x = 2                y = 2(2) - 2 = 2
 
  when x is -2/5, y =
     when x is 2, y =2