Earlier we have learned to write a set in different forms, studied operations on sets and Venn diagrams,. In Coordinate System you will learn about Ordered Pair. Usually, Ordered Pair is used to locate a point in the Coordinate System. In Order Pair, we have a pair of integers in which the first one is called abscissa and the second one is called the ordinate.
Ordered Pair (3, 4) is not equal to the Ordered Pair (4, 3). Thus, Order in a Pair is important and Order Pair contains two elements written in a fixed order.
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Ordered Pairs Definition
Pair of elements that occur in a particular order and enclosed within brackets is called a set of ordered pairs.
Let us consider a, b are two elements an Ordered Pair is represented as (a, b) where a is called the first component and b is called the second component. If Position of Components is Changed then Ordered Pair is Changed i.e it becomes (b, a) then (a, b) ≠ (b, a).
Equality of Ordered Pairs
Two Ordered Pairs are said to be equal if the corresponding first components are equal alongside the corresponding second components are equal. Consider two ordered pairs (u, v) and (x,y). The two ordered pairs are equal only if u = x, v = y i.e. (u, v) = (x, y).
Solved Examples
1. Find the values of (2x – 2, y – 1) = (x + 3, 4)?
Solution:
As per the equality of ordered pairs, the two ordered pairs will be equal only if the corresponding first components and second components are equal.
As per the above statement, we can write the equation as
2x-2 = x+3 , y-1 = 4
Solve the expressions and find the values of x, y easily
2x-x = 3+2
x = 5
y-1= 4
y = 4+1
y = 5
Therefore, the values of x, y are 5, 5.
2. If (4a, 4) = (3a+2, b – 1) find the values of a, b?
Solution:
As per the equality of ordered pairs, the two ordered pairs will be equal only if the corresponding first components and second components are equal.
As per the above statement, we can write the equation as
4a = 3a+2
4a-3a = 2
a = 2
4 = b-1
4+1 = b
4 = b-1
b =5
Therefore, the values of a, b are 2, 5.
3. What is the value of x, y if Ordered Pairs (x, y) and (3, 5) are equal?
Solution:
As per the equality of ordered pairs, the two ordered pairs will be equal only if the corresponding first components and second components are equal.
(x,y) = (3, 5)
The values of x, y are 3, 5.