Answer
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Hint: Ordered pairs are pairs of two numbers that are related to each other. We can say that ordered pairs are associated with a particular relation. Suppose we have two numbers or variables (say x and y) and we say that x and y are related to each and form an ordered pair (x , y).
Complete step by step solution:
In the above question, it is given that the elements of the ordered pairs (x , y) are related as $-x+2y=6$ ….. (i).
This means that every x and y of all the ordered pairs satisfy the given equation (i).
In the first order pair (-2 , ), we can see that $x=-2$.
Therefore, substitute $x=-2$ in equation (i).
$-(-2)+2y=6$
$\Rightarrow y=2$.
With this we get that the first ordered pair is (-2 , 2).Let us do the same procedure for the second ordered pair. Now, the ordered pair is (0 , ).This means that $x=0$.Hence, substitute $x=0$ in equation (i).
$-(0)+2y=6$
$\Rightarrow y=3$
This means that the second ordered pair is (0 , 3).
The third pair is given to be ( , 4). This means that $y=4$.
Substitute $y=4$ in equation (i).
$-x+2(4)=6$
$\therefore x=2$
This means that the third ordered pair is (2 , 4).
Therefore, the three ordered pairs associated to the given relation are (-2 , 3), (0 , 4), (2 , 4).
Note: There is another way by which we can find the order related to the given formula between x and y. We see that the given relation be x and y is in the form $ax+by+c=0$ and we know that $ax+by+c=0$ represents a straight line. Therefore, we can plot the straight line with the help of the equation. Here, the ordered pairs will be the coordinates lying on the line.
Complete step by step solution:
In the above question, it is given that the elements of the ordered pairs (x , y) are related as $-x+2y=6$ ….. (i).
This means that every x and y of all the ordered pairs satisfy the given equation (i).
In the first order pair (-2 , ), we can see that $x=-2$.
Therefore, substitute $x=-2$ in equation (i).
$-(-2)+2y=6$
$\Rightarrow y=2$.
With this we get that the first ordered pair is (-2 , 2).Let us do the same procedure for the second ordered pair. Now, the ordered pair is (0 , ).This means that $x=0$.Hence, substitute $x=0$ in equation (i).
$-(0)+2y=6$
$\Rightarrow y=3$
This means that the second ordered pair is (0 , 3).
The third pair is given to be ( , 4). This means that $y=4$.
Substitute $y=4$ in equation (i).
$-x+2(4)=6$
$\therefore x=2$
This means that the third ordered pair is (2 , 4).
Therefore, the three ordered pairs associated to the given relation are (-2 , 3), (0 , 4), (2 , 4).
Note: There is another way by which we can find the order related to the given formula between x and y. We see that the given relation be x and y is in the form $ax+by+c=0$ and we know that $ax+by+c=0$ represents a straight line. Therefore, we can plot the straight line with the help of the equation. Here, the ordered pairs will be the coordinates lying on the line.
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