Week 3 and 4 – Jss 3 Second Term Mathematics Notes

WEEK 3
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 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 equal coefficient but with 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 elimination method you may need to multiply one or both of the equations by a number in order to obtain a variable with e 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 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

 
  WEEK 4
SOLVING SIMULTANEOUS EQUATION GRAPHICALLY
To solve simultaneous equations graphically.

1. Make a table of values for both equations.
2. Draw the graphs for both equations on the same axes
3. Find the co-ordinate (i.e x and y values) where both graphs intersect these values are the solutions of both equations.
4. Check your solutions by putting these values into the original equations to make sure they satisfy them.

Example 16.3
Solve the simultaneous equations.
X – 2y = 4 and 2x – y = 5 graphically
Solution
In each equation make y the subject of the equation
(i)     x – 2y = 4
    -2y = 4 – x
     y = -2 + 0.5x ……………… (1)