• [ended]Mathematics Tutoring Session #8 Linear Equation on Thur. 25th Feb 2016 @ 3:00 - 4:00pm

    Mathematics

    Emmanuel Iwara(Tutor)
    25-02-2016 13:01:00 +0000

    Good 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. 4x-3 = 4-2x

    Example 1. Solve 4(x-3) = 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) - (3x-3) / 10 = 2

    Cross - multiplying gives

    (2x + 2) - (3x-3) = 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 = x-3, son = y-5

    Then x-3 = 2(y-5)

    x-3 = 2y - 10

    x-2y = -10 + 3

    x-2y = -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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