
[ended]Mathematics Tutoring Session #8 Linear Equation on Thur. 25th Feb 2016 @ 3:00  4:00pm
Mathematics
Emmanuel Iwara(Tutor)
25022016 13:01:00 +0000Good day all
This session has ended for today
The concept of Linear Equation is the most fundamental in mathematics often tested on JAMB and other exams. so lets take a quick look into this topics.
Equation Is a mathematical statement that shows equality between two expressions.
Linear Equation Is a mathematical statement that contains only terms in one variable and constant,and the highest power of the variable is 1.
E.g. 4x3 = 42x
Example 1. Solve 4(x3) = 2(3x 5)
Soln
Expanding and collection of like terms, yield
4x 12 = 6x 10
= 12 + 10 = 6x  4x
2 = 2x
x = 2/2 = 1.
Example 2. Solve the equation x +1 / 5  3(x  1) /10 = 2
Solution
The L.C.M, of 5 and 10 is 10, simplifying will yield
. 2(x +1)  (3x3) / 10 = 2
Cross  multiplying gives
(2x + 2)  (3x3) = 10 x 2
2x + 2  3x + 3 = 20
collecting like terms
x + 5 = 20
x = 20  5
x = 15
x = 15
WORD PROBLEMS
Some statements can be expressed in a mathematical form which will not change the meaning of what is contained in the original statement.
Example 1. A man is five times as old as his son. In five years times he will be thrice as old.What are their ages now?
Solution
Let the son's age be x. Then the father's age will be 5x.
In five years time their age will be,
Son = x + 5.
Father = 5x + 5
But 5x + 5 is thrice x + 5
5x + 5 = 3(x+5)
Expanding and collecting terms
5x + 5 = 3x + 15
2x = 15  5
2x = 10
x = 10/2 = 5
Therefore Son age = 5years.
Father age = 5x = 5 x 5 = 25years.
Example 2.Three years ago, a father was twice as old as his son, now, their combined ages amount to 11years.
Find the present age of the father.
Solution
Let father age be x, and the son age be = y
Three years ago, father = x3, son = y5
Then x3 = 2(y5)
x3 = 2y  10
x2y = 10 + 3
x2y = 7(1)
now their combined age will be x + y = 11(2)
Solving simultaneously
(2)  (1)
x + y  x + 2y = 11 (7)
3y = 18
y = 18/3 = 6
Putting (y) into equ(2)
x = 11 6 = 5 = Present Age of the father.
Example 3.When the same number is subtracted from the numerator and denominator of the fraction ^{18}/_{20}, the result is ^{11}/_{13} ,find the number.
Solution
Let the number be x, then we have
18  x / 20  x = ^{11}/_{13}
Cross  multiplying we have
13 (18  x) = 11 ( 20  x)
234 13x = 220  11x
Collecting like terms
234 220 = 11x + 13x
14 = 2x
x = 14/2 = 7
Can anyone try solving the Questions below;
(a) Add the same number to the numerator and denominator of ^{3}/_{18}. If the resulting fraction is ^{1}/_{2}. Jamb Number Question(48), 1978.
(b) Solve 1 / x + 1  1 / x+3 = 1/4
Jamb Question Number (20),1981.
(c) Five years ago, a father was 3times as old as his son, now, their combined ages amount to 110 years. thus,the present age of the father is(Jamb Question Number (13),1978).
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