Linear Equations II ( Maths)

A linear algebraic term is a term comprising one unknown (variable) raised to the power of 1. A linear equation in two variables is an equation involving two linear algebraic terms.

e.g  3x + y = 10
       5m = 3n

The units used in all terms in the equation must be of the same.

e.g Abu bought x pencil each at 90 sen and y exercise book at RM1.90 each. He paid a total of RM34.00.

The following linear equation represents the above situation:

90x  + 190y  = 3400


You can simplify the equation to:
9x + 19y = 340

EXERCISES




QUESTION #1:

During Chinese New Year, Wendy wanted to give her neighbours a box of mandarin orange. She could only spend RM130.00. The price list is as follows:

Large orange - RM30 per box
Medium orange - RM25 per box

How many boxes of medium and large oranges  could Wendy buy?


SOLUTION #1

Let large orange box quantity be X and medium orange box quantity be Y.

X + Y = 5      [ total number of neighbours]
therefore X = 5 - Y    --------[1]

30 X + 25 Y = 130   -------{2]    [ price of each multiply with box quantities equals to the maximum  amount Wendy can spend]

Substitute [1] into [2]

30 (5 - Y) + 25Y = 130
150 - 30Y + 25Y = 130
                    -5Y  = -20
                         Y = 4

Substitute Y = 4 in [1]
X = 5 - (4) =1

The answer is X = 1 and Y = 4


QUESTION #2:

Four years ago Sherry was three times as old as her daughter. Six years from now she will be twice as old as her daughter. Find out the present age of  Sherry and her daughter.



SOLUTION #2:

Let Sherry's age be, M and her daugther's age be N

M - 4 = 3 (N - 4)
M - 4 = 3N - 12
M - 3N = -8    ---------[1]

M + 6 = 2( N + 6)
M + 6 = 2N + 12
M - 2N = 6    ---------[2]

[1] - [2]

-3N + 2N = -8 - 6
         - N  = -14
            N = 14

Substitute N=14 in [1]
M-3(14) = -8
M - 42  = -8
M  = 42 - 8
M = 34

The answer is M = 34 and N = 14


QUESTION #3

The sum of two numbers  is equal to 14. The difference between the numbers is the square of 2. What are the two numbers?



SOLUTION #3:

x + y = 14  -------[1]

x - y = 4 ( 4 is square of 2)   -----[2]

[2] - [1]

-y-y = 4-14
   -2y = -10
      y = 5

Substitute y = 5 into [1]
x + 5 = 14
    x  = 14 - 5
    x  =  9 


The answer is x = 9 and y = 5