Ordered Pair Calculator: All you need to know

The Ordered Pairs Calculator is a free online calculator. It displays the ordered pair for a given equation. Any online ordered pairs calculator tool speeds up the computation. Also, it shows the ordered pairs in a matter of seconds.

An ordered pair (x, y) indicates a specific point in a coordinate plane. So, the first number represents the x-axis. Then, the second number represents the y-axis. We usually write the x coordinate value first.

In this article, we are talking about thIs topic. So, keep reading to know more about it.

Ordered pair calculator

An ordered pair, as the name implies, is a pair of items that are important for the order in which they are placed. In coordinate geometry, ordered pairs are commonly used to represent a point on a coordinate plane. They are also used to symbolise components of a relationship.

Read Also: Adjacent Angles: Meaning, Examples

An ordered pair is made up of two items separated by a comma and written between the parentheses. (x, y) represents an ordered pair, where ‘x’ is the first element and ‘y’ is the second member in the ordered pair. These components have different names depending on the context, and they can be either variables or constants. In an ordered pair, the order of the elements is important. It indicates that (x, y) may not always be equivalent to (y, x). Ordered pairs include (2, 5), (a, b), (0, -5), and so on.

Ordered pair calculator online free

To get the ordered pair for any equation, substitute any integer or rational number for one of the variables and solve for the remaining variable. This results in values for both variables that fulfil the specified equation. Then, both of the variable’s resultant values are represented in the form of (x, y), and this representation is known as an ordered pair.

Sorted pairs A pair of items is an Ordered pair (a, b). The order of the objects in the pair matters: the ordered pair (a, b) differs from the ordered pair (b, a) unless a = b. (The unordered pair a, b, on the other hand, equals the unordered pair b, a.)

Ordered pair calculator steps

To use the calculator, follow the procedures below:

  • First, fill in the blanks with the equation and the one coordinate of the ordered pair (enter the unknown as x).
  • Then, press the “Calculate” button to get the value of y in relation to x.
  • Atlast, press the “Reset” button to clear the box and input new values.

Ordered pair calculator graphing

We now understand the distinction between an ordered pair’s x- and y-coordinates in coordinate geometry. Let us now look at how to graph ordered pairs.

  • Always begin at the origin and progress horizontally by |x| units to the right if x is positive and left if x is negative. Stay put.
  • Begin where you left off in Step 1 and travel vertically by |y| units up if y is positive and downward if y is negative. Stay put.
  • Put a dot precisely where you ended in Step 2, and that dot symbolises the ordered pair (x, y).
  • |x| and |y| denote the absolute values of x and y in these stages.

Begin at the origin, travel 4 units to the right (since 4 is positive), and then 3 units down (as 3 is negative). The order of the elements in an ordered pair is significant, which is why it is called an “ordered” pair. As illustrated below, (4, -3) and (-3, 4) are positioned at various points on the plane.

Ordered pair calculator sets

We’ve seen how ordered pairs are utilised in coordinate geometry to find a point. They are, however, employed in set theory in a different sense. The cartesian product is the collection of all feasible ordered pairings from set A to set B. If A = 1, 2, 3 and B = a, b, c, then the cartesian product is A x B = (1, a), (1, b), (1, c), (2, a), (2, b), (2, c), (3, a), (3, b), (3, c), and it is a set created by all ordered pairings (x, y) where x is in A and y is in B. A relation is any subset of the cartesian product.

A relation is, for example, (1, a), (1, b), (3, c).

  • First, if the expression (2, 4) pertains to the relation “divides,” it signifies that 2 divides 4.
  • Then, If the relation (4, 2) is “more than,” it signifies that 4 is greater than 2.
  • Then, If (x, y) belongs to the relation “is a sister of,” then x is the sister of y.

Ordered pair calculator from equation

Example 1

y = 4x + 5 is the provided equation. What is the value of y if the value of x is 5? Fill in the blanks with your response in the ordered pair format.

Solution:

Given that y = 4x + 5……….. (1)

Moreover, x = 5.

Putting x = 5 into the equation (1)

4(5) + 5 = y

Then, 20 + 5 Equals y

Then, 25 = y

As a result, the ordered pair for the equation is (5, 25).

Example 2

Example 1: Draw a point using the ordered pair (-2, 3). Indicate the quadrant in which it is located.

Solution: Plot the point (-2, 3) as follows:

  • Move 2 units to the left of the origin (as -2 is negative)
  • As a result, move three units up (as 3 is positive)
  • Put a dot where you’ve arrived.

Answer: We plotted (-2, 3), which is in Quadrant II.

Example 3

Determine the x and y values if (2x – 3, 3y + 2) = (5, 8).

It is established that (2x – 3, 3y + 2) = (5, 8).

According to the ordered pair equality property, 2x – 3 = 5… (1) 3y + 2 = 8… (2)

Derived from (1),

x = 4 or 2x = 8

Derived from (2),

3y = 6 (or) 2y

x = 4, y=2 is the answer.

Example 4

Example 3: Without charting the ordered pairings, identify the quadrants in which they are located. (2, -3) (a) (b) (-2, -3).

Solution:

The x-coordinate in (2, -3) is positive, whereas the y-coordinate is negative. As a result, it is located in Quadrant IV.

Both the x and y coordinates are negative in (-2, -3). As a result, it is located in Quadrant III.

Answer: (a) is in IV, and (b) is in III.

Example 5

Consider the following first-order equation: 2x + 6

Take x = 1 in this case.

As a result, the equation is 2 + 6 = 8.

Consider x = 2 once again.

4 + 6 = 10 will be the equation.

As a result, the two ordered pairs of the equation are (1, 8) and (2, 10).

Ordered pair calculator pairs

If (x, y) = (a, b) for any two ordered pairs (x, y) and (a, b) (either in coordinate geometry or in relations), then x = a and y = b. In other words, if two ordered pairs are equal, their corresponding elements are also equal. This is known as the “equality property of ordered pairs.” As an example:

Ordered Pair Calculator

  • First, If (x, y) = (2, -3), then x equals 2 and y equals -3.
  • Then, If (x + 1, y – 2) equals (-3, 5), then x + 1 equals -3 and y – 2 equals 5.
  • Then, In coordinate geometry, an ordered pair (x, y) is used to indicate the position of a point, where x is the horizontal distance and y is the vertical distance.
  • Also, an ordered pair (x, y) represents a component of the relation R represented by xRy (x “is related to” y).
  • Then, if (x, y) = (a, b), then x equals a and y equals b.

Ordered pair calculator geometry

In coordinate geometry, we used an ordered pair to indicate the location of a point on the coordinate plane with respect to the origin. Then, Two intersecting perpendicular lines produced a coordinate plane. So, one of which is horizontal (x-axis) and the other vertical (y-axis). The origin is the place where both axes cross. An ordered pair (x, y) represents every point on the coordinate plane, with the first element x. So, x is the x-coordinate and the second element y is the y-coordinate. More distinctions between the elements of the ordered pair utilised in geometry may be seen here.

First Element of Ordered PairSecond Element of Ordered Pair
It is x-coordinate.So, It is y-coordinate.
So, it has another name. This is “abscissa”.Also, it has another name. This is “ordinate”.
It represents the horizontal distance of the point from the origin.It represents the vertical distance of the point from the origin.
This number is one of the numbers on the x-axis.This number is one of the numbers on the y-axis.
It represents the distance of the point from the y-axis.It represents the distance of the point from the x-axis.
Example:

If (2, 4) is a point on the coordinate plane, then 2 is the distance of the point from the y-axis.

 

Example:

If (2, 4) is a point on the coordinate plane, then 2 is the distance of the point from the y-axis.

Ordered pair calculator algebra

So, a relation in mathematics is any collection of ordered pairs. Also, the ordered nature of the pairings is significant. Then, It implies that the ordered pair (a, b) differs from the ordered pair (b, a) unless a = b. So, the elements of the ordered pairs, naturally connected or related in some way for the majority of meaningful relations.

Then, in more technical terms, a relation is a subset of the set of all possible ordered pairs (a, b). So, the first element of each ordered pair is drawn from one set (call it A). Then, the second element of each ordered pair is drawn from a different set (call it B). So, A and B are frequently the same set; A = B is common.

Then, the set of all such ordered pairs is created by taking the first element from the set A. Also, the second element from the set B is known as the Cartesian product of the sets A and B. The symbol A B denoted it. A relation between two sets, a specified subset of their Cartesian product.

Ordered Pair Calculator

Because relations are set at ordered pairs. Also, they can be graphed on the ordinary coordinate plane. It happens if their elements are ordered pairs of real numbers. For example, the relation consisting of ordered pairs (x, y) such that x = y is a subset of the plane, specifically those points on the line x=y.

Ordered pair calculator Example

Figure 1 is another illustration of a relationship between real numbers. Hans and Cassidy created the illustration. We provided the image of the set of ordered pairs (x, y) in which x is greater than y. This is also a subset of the coordinate plane, the half-plane below and to the right of the line x = y, excluding the line’s points. Because a relation is a subset of all possible ordered pairs (a, b), certain elements of the set A may not occur in any ordered pairs of a specific relation. Similarly, certain members of the set B may not appear in any of the relation’s ordered pairs.

The collection of all those members of the set A that appear in at least one ordered pair of a relation form a subset of A called the domain of the relation. The collection of members from the set B that appear in at least one ordered pair of the relation form a subset of B called the range of the relation. Elements in the range of a relation are called values of the relation. One special and useful type of relation, called a function, is very important. For every ordered pair (a, b) in a relation, if every a is associated with one and only one b, then the relation is a function.

In other words, a function is a relation in which no two ordered pairs have the same initial element. All kinds of connections and functions are significant in every discipline of study because they are mathematical formulations of the physical interactions we find in nature.

Ordered pair calculator variables

An ordered pair is a set of numbers in a certain order. For example, ordered pairs are (1, 2) and (- 4, 12). The order of the two numbers matters: (1, 2) is not the same as (2, 1) — (1, 2)≠(2, 1).

Ordered pairs represented two variables. We mean x = 7 and y = -2 when we write (x, y) = (7, -2). The x-coordinate is the number that corresponds to the value of x, and the y-coordinate is the number that corresponds to the value of y.

Example 1

Given that (x, y) = (-1, 4), what is the value of 3x + 2y – 4?

3x + 2y – 4 = 3(- 1) + 2(4) – 4 = – 3 + 8 – 4 = 1

Example 2

Which of the following ordered pairs (x, y) is a solution to the equation – 6 = 1? (4, 1), (5, 2), (-3, 1), (-3, -1), (1, 4)

  • First, (x, y) = (4, 1): -6 =  – 6 = 7 – 6 = 1. Solution.
  • Then, (x, y) = (5, 2): -6 =  -6 =  -6 = – ≠1. Not a solution.
  • Then, (x, y) = (- 3, 1): -6 =  -6 = – 7 – 6 = – 13≠1. Not a solution.
  • Also, (x, y) = (- 3, – 1): -6 =  – 6 = 7 – 6 = 1. Solution.
  • Then, (x, y) = (1, 4): -6 =  -6 =  -6 = – ≠1. Not a solution.

Thus, {(4, 1),(- 3, -1)} are solutions to  – 6 = 1.

Ordered pair calculator with solution

We need two sets of equations to solve for two variables (usually denoted as “x” and “y”). Assuming you have two equations, the substitution approach is the best way to solve for both variables. This method entails solving for one variable as far as feasible, then inserting it back into the other equation. Knowing how to solve a system of equations with two variables is useful in a variety of situations, including attempting to discover the coordinates for points on a graph.

Make two equations with the two variables you wish to solve. In this example, we will calculate the values for “x” and “y” in the equations “3x + y = 2” and “x + 5y = 20.”

Solve one of the equations for one of the variables. Let’s solve for “y” in the first equation for this case. To obtain “y = 2 – 3x,” subtract 3x from either side.

Ordered Pair Calculator

In order to determine the x value, plug the y value from the first equation into the second equation. In the above example, this indicates that the second equation is “x + 5(2- 3x) = 20.”

Calculate x. “x + 10 – 15x = 20,” which is subsequently “-14 x + 10 = 20,” becomes the example equation. Subtract 10 from each side and divide by 14 to get x = -10/14, which simplifies to x = -5/7.

To determine the y value, plug the x value into the first equation.

y = 2 – 3(-5/7) equals 2 + 15/7, or 29/7.

Some frequently asked questions

How do you find the ordered pair?

We can see the coordinates of one point in the coordinate system in an ordered pair. A points ordered pair of (x, y) identified A point. The first number represents the x-coordinate, while the second represents the y-coordinate. To graph a point, you draw a dot at the coordinates of the ordered pair.

What is the ordered pair calculator?

The Ordered Pairs Calculator is a free online calculator. It displays the ordered pair for a given equation. Any online ordered pairs calculator tool speeds up the computation. Also, it shows the ordered pairs in a matter of seconds. An ordered pair (x, y) indicates a specific point in a coordinate plane. So, the first number represents the x-axis. Then, the second number represents the y-axis. We usually write the x coordinate value first.

What is an ordered pair with an example?

y = 4x + 5 is the provided equation. What is the value of y if the value of x is 5? Fill in the blanks with your response in the ordered pair format.

Solution:

Given that y = 4x + 5……….. (1)

Moreover, x = 5.

Putting x = 5 into the equation (1)

4(5) + 5 = y

20 + 5 Equals y

25 = y

As a result, the ordered pair for the equation is (5, 25).

Which ordered pair is a solution of the equation y =- 3x 4?

As a result, the notation (x, y), employed to describe ordered pairs in the equation y = 3x – 4. The specific ordered pairings that meet the equation from the above values are (1, -1), (0, -4), (3, 5), and (-2, -10).

Is a set of ordered pairs XY?

A relation is just a collection of ordered pairs (x,y). In formal mathematics, a function is a relation in which x1=x2 if (x1,y) and (x2,y) are both in the relation. This simply states that two ordered pairs with the same x -value but distinct y -values cannot exist in a function.

How do you find B with two ordered pairs?

To find the y-intercept, use the slope and one of the points (b). One of your points can substitute for the x and y, and the slope you just computed can substitute for the m in your equation y = mx + b. The only variable remaining is b. To solve for b, use the techniques you’re familiar with for solving variables.

How do you read XY coordinates?

Coordinates, expressed as (x, y), which means the x axis point comes first. Then, the y axis point followed it. Some people remember this by saying “along the corridor, up the stairs”. So, it means to follow the x axis first and then the y.

What is a function calculator?

This is a free online tool. So, it displays the graph of a specified function. Then, any online function calculator tool speeds up the calculations. Also, it presents the graph of the function by computing the x and y-intercept values, as well as the slope values, in a matter of seconds.

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