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.
