Page 105 - Mathematics

2. Write the two simultaneous equations Hence, y = 48
according to the requirements of the Therefore, the son’s age is 12 years
problem. and the father’s age is 48 years.
3. Solve the linear simultaneous
equations. Example 5.39
4. Give the conclusion according to Tanzania Institute of Education
the demand of the problem. The sum of two numbers is 30.
The difference between the larger
Example 5.38 number and three times the smaller
number is 2. Find the two numbers.
The age of a father is four times Solution
the age of his son. If the sum of
their ages is 60 years, find the age Let x be the larger number and y be
of the son and that of the father. the smaller number.
Thus,
Solution
Let x be the age of the son and y be  x y+= 30 (i)

the age of the father.  x − 3y = 2 (ii)

It follows that, Solve equations (i) and (ii)
y = 4x (i) simultaneously using elimination
y
x += 60 (ii) method.
Substituting equation (i) into Eliminate x to obtain an equation
equation (ii) gives, in one variable. That is,
y
x + 4x = 60 −  x += 30

5x = 60  x − 3y = 2
60
x = 4y = 28
5 y = 28
= 12. 4

Hence, x = 12. 7=
Substituting x = 12 into equation Hence, y = 7.
(i) gives, Substitute the value of y in equation
y = 4 12× (i) or (ii). From x y+= 30, Mathematics Form One
7
= 48 x += 30
x = 23

99

25/10/2024 09:51:34
Mathematics form 1.indd 99 25/10/2024 09:51:34
Mathematics form 1.indd 99