Page 106 - Mathematics_F1

3. Solve the linear simultaneous Example 5.38
equations.
4. Give the conclusion according to The sum of two numbers is 30.
The difference between the larger
the demand of the problem. number and three times the smaller
number is 2. Find the two numbers.
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Example 5.37 Solution Tanzania Institute of Education
Let the large number be x .
The age of a father is four times Let the small number be y.
the age of his son. If the sum of Thus,
their ages is 60 years, find the age x +  y = 30 (1)
of the son and that of the father. 
 x − 3y = 2 (2)
Solution Solve (1) and (2) by any method.
Let x be the age of the son and y be In this case, elimination method
the age of the father. is used.

It follows that, Eliminate the variable x to get y:
30
y =
x + 
y = 4x (1) −  x − 3y = 2

y
x += 60 (2) x – x + y – (–3y) = 30 – 2
Substituting equation (1) into 4y = 28
28
equation (2) gives, y = .
_
4
x + 4x = 60 Hence, y = 7.
5x = 60 Eliminate the variable y to get x
60
x = Multiply (1) by 3 and (2) by 1:
5 3( +  ) = 30 3
×
= 12.  1( − 3 ) = 2 1
×

Hence, x = 12.
3x +  3y = 90 (3)
Substituting x = 12 into equation  x − 3y = 2
(1) gives,  (4)
y = 4 12× Add (3) and (4):

= 48 +  3x +  3y = 90
Hence, y = 48  x − 3y = 2
3x + x + 3y + (–3y) = 90 + 2 Mathematics Form One
Therefore, the son’s age is 12 years 4x = 92
and the father’s age is 48 years.
92
_
x = .
4

99

25/09/2025 15:01:16
Mathematics form 1.indd 99 25/09/2025 15:01:16
Mathematics form 1.indd 99