Introduction to ordered pair math:
An ordered pair in math is the pair of two objects which occur in a particular order.
That is, here that order is very important.
Ex: Let 7 and 9 be two numbers. Then (7, 9) is one ordered pair and (9, 7) is another ordered pair. Hence in (7, 9) we call 7 as the first component and 9 as the second component.
Two ordered pairs are said to be equal if they have the same first components and the same second components.
Ex: (- 7, 11) = (- 7, 11) and (5, 8) = (5, 8).
Suppose (x, y) = (4, 3). Then x = 4, y =3.
Now let us see few problems on these concepts.
Algebra is widely used in day to day activities watch out for my forthcoming posts on algebra 2 problems and answers and algebra 2 formulas list. I am sure they will be helpful.
Example Problems on Ordered Pair Math:
Ex 1: By using the set A = {a, b}, form all possible ordered pairs.
Solution: Given: A = {a, b}.
Therefore the ordered pairs are {(a, a), (a, b), (b, a), (b, b)}.
Ex 2: Find all possible ordered pair from X = {1, 2, 3}.
Solution: Given: X = {1, 2, 3}.
Therefore the possible ordered pairs are given by { (1,1), (1,2 ), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3) }
Ex 3: If (3a – 5, 8b +7) = (7, 23), Find the value of ‘a’ and ‘b’.
Solution: Given: (3a – 5, 8b +7) = (7, 23)
`implies` 3a -5 = 7 and 8b + 7 = 23
`implies` 3a = 5+7 and 8b = 23 – 7
`implies ` 3a = 12 and 8b = 16
`implies` a = `12/3` = 4 and b = `16/8` = 2.
Therefore a = 4 and b = 2.
Ex 4: If (3a, - 5) = (a -2, b+3), find the values of ‘a’ and ‘b’.
Solution: Given: (3a, -5) = (a- 2, b+3)
`implies` 3a = a – 2 and -5 = b+3
`implies ` 3a – a = - 2 and -5 – 3 = b
`implies` 2a = - 2 and b = - 8
`implies` a = `-2/2` = - 1 and b = -8.
Therefore a = -1, b = - 8.
Practice Problems on Ordered Pair Math:
1. If (x – 3, x + 2y) = (3x -1, 3), Find the value of x and y.
[Ans: x = -1, y = 5/2]
2. If (3a – 2) 5 – b) = (4, - 1), find a and b.
[Ans: a = 2, b = 6].
An ordered pair in math is the pair of two objects which occur in a particular order.
That is, here that order is very important.
Ex: Let 7 and 9 be two numbers. Then (7, 9) is one ordered pair and (9, 7) is another ordered pair. Hence in (7, 9) we call 7 as the first component and 9 as the second component.
Two ordered pairs are said to be equal if they have the same first components and the same second components.
Ex: (- 7, 11) = (- 7, 11) and (5, 8) = (5, 8).
Suppose (x, y) = (4, 3). Then x = 4, y =3.
Now let us see few problems on these concepts.
Algebra is widely used in day to day activities watch out for my forthcoming posts on algebra 2 problems and answers and algebra 2 formulas list. I am sure they will be helpful.
Example Problems on Ordered Pair Math:
Ex 1: By using the set A = {a, b}, form all possible ordered pairs.
Solution: Given: A = {a, b}.
Therefore the ordered pairs are {(a, a), (a, b), (b, a), (b, b)}.
Ex 2: Find all possible ordered pair from X = {1, 2, 3}.
Solution: Given: X = {1, 2, 3}.
Therefore the possible ordered pairs are given by { (1,1), (1,2 ), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3) }
Ex 3: If (3a – 5, 8b +7) = (7, 23), Find the value of ‘a’ and ‘b’.
Solution: Given: (3a – 5, 8b +7) = (7, 23)
`implies` 3a -5 = 7 and 8b + 7 = 23
`implies` 3a = 5+7 and 8b = 23 – 7
`implies ` 3a = 12 and 8b = 16
`implies` a = `12/3` = 4 and b = `16/8` = 2.
Therefore a = 4 and b = 2.
Ex 4: If (3a, - 5) = (a -2, b+3), find the values of ‘a’ and ‘b’.
Solution: Given: (3a, -5) = (a- 2, b+3)
`implies` 3a = a – 2 and -5 = b+3
`implies ` 3a – a = - 2 and -5 – 3 = b
`implies` 2a = - 2 and b = - 8
`implies` a = `-2/2` = - 1 and b = -8.
Therefore a = -1, b = - 8.
Practice Problems on Ordered Pair Math:
1. If (x – 3, x + 2y) = (3x -1, 3), Find the value of x and y.
[Ans: x = -1, y = 5/2]
2. If (3a – 2) 5 – b) = (4, - 1), find a and b.
[Ans: a = 2, b = 6].
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