Question Video: Determining Which Ordered Pairs Satisfy a Given Linear Relation Mathematics • Second Year of Preparatory School

Video Transcript

Which of the following satisfies the relation 𝑥 minus 𝑦 is equal to negative 10? Is it (A) the ordered pair negative two, negative two? (B) The ordered pair negative 16, six. (C) Nine, negative one. (D) Negative 12, negative two. Or (E) the ordered pair negative five, negative 15.

To answer this question, we try each pair of values in turn in the given equation. That’s 𝑥 minus 𝑦 is equal to negative 10. This means that from each pair, we substitute the first value for 𝑥 and the second for 𝑦. And if the right- and left-hand sides are equal, then we can say that the pair satisfies the relation 𝑥 minus 𝑦 is equal to negative 10.

So, looking first at option (A), we have 𝑥 is equal to negative two and 𝑦 is also equal to negative two. Substituting these values into our linear relation, this gives us negative two minus negative two. And we want to know, does this equal negative 10? Now, since subtracting negative two is the same as adding positive two, this gives us negative two plus two. But that’s equal to zero, which of course is not equal to negative 10. This means that our first ordered pair (A) does not satisfy the linear relation 𝑥 minus 𝑦 is equal to negative 10.

Next, we consider option (B). That’s where 𝑥 is negative 16 and 𝑦 is equal to six. Into our linear relation, this gives us negative 16 minus six. And this evaluates to negative 22, and this does not equal negative 10. And hence, we can say that option (B) does not satisfy the linear relation.

For option (C), our values are 𝑥 is nine and 𝑦 is negative one. This gives us nine minus negative one, which evaluates to 10, which is not equal to negative 10. Hence, option (C) does not satisfy the linear relation.

For option (D), our values are 𝑥 is equal to negative 12 and 𝑦 is negative two. Into our linear relation 𝑥 minus 𝑦 is equal to negative 10, this gives us negative 12 minus negative two. And since subtracting negative two is the same as adding positive two, we have negative 12 plus two, and that’s equal to negative 10. And hence, option (D) does satisfy the linear relation.

Finally, checking our option (E), this has values 𝑥 is equal to negative five and 𝑦 is negative 15, which in our linear relation give us negative five minus negative 15. And this evaluates to negative five plus 15, which is 10. Since this is not equal to negative 10, we can say that option (E) does not satisfy the linear relation 𝑥 minus 𝑦 is equal to negative 10.

We can see that only one of the given ordered pairs satisfies the relation 𝑥 minus 𝑦 is equal to negative 10, that is, option (D). Hence, the ordered pair negative 12, negative two satisfies the relation.