Week 10 and 11 – Jss 3 First Term Mathematics Lesson Notes

WEEK 10
SIMPLE EQUATIONS INVOLVING FRACTIONS
Examples: Solve the following equations

1. –
2. P =
3. = 5 +

SOLUTION

1. The L.C.M of 5 and 10 is 10 multiply both sides by 10

10 x = 10 ()        OR    we cross multiply
2 x = 8 –              =
=                     10 x = 5 x (8 –)
= 1                 = 40 –
                     =
             = 1
(b)     P =                 (c) Multiply both sides by 6
2p = 35 – 3p                6 x = 6 x 5 + 6 x
=                     3 (a-5) = 30 + 2a
P = 7                    3a – 15 = 30 + 2a
a = 45
Exercise: Solve the following equations
(a) = 5 (b) = (c) = 8 (d) + = 0
Fraction with binomial denominator
Examples
a) – 4 = 0 (b) – = 0 (c) =
SOLUTION

1. – 4 = 0            (b) – = 0        (c) =

   – 4              =              3 (2y – 1) = 5 (y + 2)
   4 (5 -) = 2             3 (2y – 3) = 20         6y – 3 = 5y + 10
   20 – 4 = 2             6y – 9 = 20            Y = 13
   4 = 18             =
   = 45             y = 4

EXERCISE
a)     + 8 = -3 (b) = 4 (c) = 1 (d) =
Simultaneous linear Equations
These are equations such as = 8 and = 6
Graphical Method
To solve simultaneous equations graphically

• Make a table of values for both equations
• Draw the graphs of both equations on the same axes
• Find the coordinate where both graph interest. This values () are the solutions of both axes

Examples: Solve the following simultaneous equations graphically (a) and (b) and r
SOLUTION

1. Y = -2 + 0.5            

        0     2      4             -1     0      5     = 2
        -2    -1    0             -7    -5    5     = -1

    

2.             

        -1     0      2             -2     0      2     = 2
        12    10     6             -6    -2     2     = -1

 Exercise

1. (b)

            
SUBSTITUTION METHOD
Examples (a) , 2X – Y = 52 (b)

SOLUTION

1.     …………1

    ………….2
Step 1: Rearrange one of the equations so that are variable is made the subject
That is from eqn I    3
Step 2: Substitute into the second equation. That is substitute and solves the resulting equation.
Into eqn…………2
– y = 5
=
Y = -1

 
 
 Step 3: Substitute your answer into 3 to find the other variable
That is

From eqn……..1 ……… 3
Substitute eqn3 into eqn 2 gives

=
= 2
From Eqn 3

EXERCISE: (b)

 ELIMINATION METHOD
Examples: (a)
When one of the unknown has equal coefficient
SOLUTION

1. …………. 1        

   +…………… 2        
   =                  – a = -5

                        a = 5
From eqn 1      from Eqn 1
                    
     =
                        
                

 
 
 Example 2 (When none of the unknown has equal coefficient)
Example:         (b)
            
SOLUTION

1. To make the coefficients of x equal multiply eqn 1 by 2 and eqn 2 by 1

   2 x 1    ……….. 3
   1 x 2 …………. 4
        =
       

    From Eqn 1
       
       
           

2.     ——-1

    ——-2
    4 x 1        ——–3
    3 x 2     …………….4
From Eqn (1)

     =

EXERCISE: ,
WORD PROBLEMS
EXAMPLES

1. The sum of two numbers is 30 and their difference is 15. Find the two numbers
2. 3 boxes and 2 packages weigh 1240g while 5 boxes and 7 packages weigh 2800g. What is the weight of a box and a package?

SOLUTION

1.             (2)

            
                
                
                     =
                    
From (1)
            
                
    
Exercise:

1. The sum of two numbers is 18 and their difference is 12. Find the two numbers
2. This shape is an equilateral triangle with dimension show finds its perimeter.

   

-2 4x – y + 1

1. Andre has more money than Bob. If Andre gave Bob $20, they would have the same amount. While if Bob gave Andre $22, Andre would then have twice as much as Bob. How much does each one actually have?
2. In a two digit number. The units digit is thrice the tens digit. If 36 is added to the number, the digits interchange their place. Find the number.
3. If 2 is added to the numerator and denominator it becomes 9/10 and if 3 is subtracted from the numerator and denominator it become 4/5. Find the fractions.

ASSIGNMENT:
EXERCISE 15.5; NO 2 – 5.PAGE 127

 WEEK 11
REVISION and EXAMINATION