Ordered Number Pairs

Introduction to Ordered Number Pairs:

The numbers can be written in certain order inside the parenthesis like (x, y). Ordered pair is one of the branches of algebra in math. A number pair (x, y) is located in any point or an object in a plane is called as an ordered number pair. Ordered pairs consists of two terms such as x and y. Here, the position of the terms cannot be changed unless it is equal. Ordered pairs are otherwise called as co-ordinates.

Finding Ordered Number Pairs

Depending upon the given number of equations, the procedure should be changed to learn the difference of solving the ordered pairs.

1. If only one equation is given, we have to convert the equation in below format like,

y = a1x +c,

Substitute the values for x and find the value of y.

Here, x is said to be substituted value and y is an obtained value.

Therefore, many values can be obtained for different x values.

2. If it is more than two equations is given,

Solve the equations and find out the values of x and y, then (x, y) is an ordered pair.

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Worked Examples to Ordered Number Pairs

Problem 1:

Find the ordered number pairs of the equation y - 3x = 2

Solution:

Step 1:

Let us write the given equation as

y  - 3x = 2.

Step 2:

Change the above equation into y = 2 + 3x,

Substitute x = 0

y = 2 + 3(0),

y = 2

Therefore, the ordered pair (x, y) is (0, 1).

Step 3:


Substitute x = 1 in the equation, we get,

y = 2 + 3(1),

y = 2 + 3 = 5

Therefore, the ordered pair (x, y) is (1, 5).

Step 4:

Substitute x = 2 in the equation, we get,

y = 2 + 3(2)

y = 2 + 6 = 8

Therefore, the ordered pair (x, y) is (2, 8).

Step 5:

Substitute x = 3 in the equation we get,

y = 2 + 3(3)

y = 2 + 9 = 11

Therefore, the ordered pair (x, y) is (3, 11).

Step 6:

Substitute x = 4 in the equation, we get,

y = 2 + 3(4),

y = 2 + 12

Therefore the ordered pair (x, y) is (4, 14).

Problem 2:

Find the ordered pair of the equations

2x + 3y = 6

3x + 5y = 4

Solution:

Step 1:

Let's start with 2x + 3y = 6 for the variable x.

Step 2:

Move the 3y to the right hand side by subtracting 3y on both sides, like this,

2x = 6 – 3y

Step 3:

To isolate x value, we have to divide both sides of the equation by 2 nearer to the x variable on the left hand side. The last step is to divide both sides of the equation by 2, we get,

x =6/2-(3/2)y

x = 3 – (3/2)y

Step 4:

Next, let's solve 3x + 5y = 4 for the variable y.

Step 5:

Move the 3x to the right hand side by subtracting 3x on both sides, like this,

5y = 4 – 3x

Step 6:

To isolate the y value, we have to divide both sides of the equation by 5 nearer to the y variable on left hand side of the equation. The last step is to divide both sides of the equation by 6, we get,

y = 4/5 - (3/5)x

Step 7:

Now, plug the x result, x = 3 – (3/2)y in y, we get,

This gives y = 4/5 - (3/5)(3 – (3/2)y)

4/5 – 9/5 – (9/10)y

-9y/10 = 9/5 – 4/5

-9y/10 = 5/5

-9y/10 = 1

-9y = 10

y = - 10/9

Step 8:

Plug the value of y in the x equation we get,

x = 3 - (3/2)(- 10/9)

x = 3 + 30/18

x = 3 + 15/9

x = 3 + 5/3

x = (9 + 5)/3

x = 14/3

Therefore, the solution for ordered number pair is (14/3, -10/9).