Page 117 - Mathematics

14. Solve each of the following 18. Two numbers are such that, one
simultaneous equations by using number is greater than the other.
elimination method. If 25 is subtracted from the greater
3x −  2y = 17 number, the result is half the
(a) 

 x + 2y = 11 smaller number. When the two Tanzania Institute of Education
5x −  3y = 19 numbers are added, the result is
(b) 
 4x − 3y = 14 91. Find the two numbers.
 0.1x + 0.2y = 1.1 19. Solve for the values of x in each
(c) 
 1.5 – 0.2x y = 10.1 of the following:
1
2
x −  2y = − 1 (a) x − > 2
(d) 
14
 3x − 4y = 3 (b) 3x +≤
15. Solve each of the following pairs (c) 5x− − 23>
1
of simultaneous equations by using (d) 1 − 4x ≤−
2
a method of your choice. 1 1 2
x
+=
 2x y 31 (e) 3 − 4 ≥ 8
(a)  3x + 2y = 52 1
3
 (f) 10x +< 2 2 x − 12
 ( 9 x – y ) – x + ( ) y = 14

(b)  20. Twice the sum of two numbers is
  ( x + ) y + ( 5 x – ) y = 28
at most 87. If one of the numbers
 4 – 2y x = 2 is 13, what is the largest possible
(c) 
 6–yx = 6 value of the second number?
 x y 21. Solve the following system of
 2 − 3 = − 1 linear simultaneous equations.

(d) 
 x + y = 5  3
  4 3 2  2 x − 0.2y = 4

16. If the sum of the ages of a father and  −+ 3y = 9

x
his daughter is 60 years, and the age   2
of the father is five times the age of 22. Formulate an algebraic equation
the daughter, find their ages. of the total number of students
17. Two numbers x and y are such that, basing on the following statement:
the sum of 2x and y is 62, while the In a class of 42 students, some of Mathematics Form One

sum of x and 2y is 79. Find the them came late, and the rest came
values of x and y. early.

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