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How do you complete these ordered pairs for this equation (-2 , ), (0 , ), ( , 4) given the formula $-x+2y=6$?

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Last updated date: 01st Mar 2024
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IVSAT 2024
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.
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