Math Ordered Pairs

Introduction to ordered pair learning:

Ordered pair learning is a topic in Algebra, which is a subdivision in mathematics. An ordered pair  represents a location (object or point) in the plane. Ordered pairs contains  two terms ‘x’ and ‘y’, represented in the form (x, y), the position of the terms cannot be interchanged unless the they are equal. Ordered pairs are also called as co-ordinates.

Learning to Find ordered pairs:

Depending upon the number of equations given the procedure to find the ordered pairs learning differs.
1. If only one equation is given,
Convert the given equation into a format,
y = a1x +c,
Then substitute different values for ‘x’ and obtain ‘y’
Form ordered pairs learning (x, y), where ‘x’ is the substituted value and ‘y’ is the obtained value.
Therefore different ordered pairs are obtained for various ‘x’ values.

2. If more than one equation is given,
Solve those equations and find out the values of ‘x’ and ‘y’,
Then (x, y) is the ordered pair

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Learning example problems to find ordered pairs

Problem 1:
Find the ordered pairs of y-2x=1
Solution:
y-2x=1,
Change the above equation into y =1+2x,
Substitute x=0
y =1+2(0),
y =1
Therefore the ordered pair (x, y) is (0, 1).
Substitute x=1
y =1+2(1),
y =3
Therefore the ordered pair (x, y) is (1, 3).
Substitute x=2
y =1+2(2),
y =5
Therefore the ordered pair (x, y) is (2, 5).
Substitute x=3
y =1+2(3),
y =7
Therefore the ordered pair (x, y) is (3, 7).
Substitute x=4
y =1+2(4),
y =9
Therefore the ordered pair (x, y) is (4, 9).

Problem 2:
Find the ordered pair of the equations,
3x+2y=5
4x+6y=3
Solution:
Let's start with 3x+2y = 5 for the variable x.
Move the 2y to the right hand side by subtracting 2y from both sides, like this:
Now, the equation reads:
3x = 5-2y
To isolate the x, we have to divide both sides of the equation by the other variables around the x on the left side of the equation.
The last step is to divide both sides of the equation by 3
The solution to your equation is:
x =5/3-(2/3)y
Next, let's solve 4x+6y = 3 for the variable y.
Move the 4x to the right hand side by subtracting 4x from both sides, like this:
Now, the equation reads:
6y = 3-4x
To isolate the ‘y’, we have to divide both sides of the equation by the other variables around the y on the left side of the equation.
The last step is to divide both sides of the equation by 6,
The solution to your equation is:
y =1/2-(2/3)x
Now, plug the earlier result, x=5/3-(2/3)y, in for x everywhere it occurs in
y=1/2-(2/3)x.
This gives y=1/2-2/3(5/3-(2/3)y). Now all we have to do is solve this for y,to have our first solution.
1/2-2/3*(5/3-(2/3)y) evaluates to ½ - 10/9 + 4y/9
Y - 4y/9 = -11/18
5y/9 =-11/18
The last step is to divide both sides of the equation by 5/9 like this:
y = - 11/18 * 9/5
The solution to the equation is:
y = -11/10
Lastly, to find the solution for x, we plug this answer for y into the earlier result that
x=5/3-(2/3)y.
This gives x=5/3-2/3(-11/10).
On, simplifying.
x= 12/5,
So, the ordered pair to given equations are:
(12/5, -11/10)