### Video Transcript

Which of the following relations
does the point negative five, two not satisfy? (A) Five π₯ plus π¦ equals negative
23. (B) Five π₯ plus two π¦ equals
zero. (C) Five π₯ plus three π¦ equals
negative 19. (D) Three π₯ minus π¦ equals
negative 17. Or (E) four π₯ plus π¦ equals
negative 18.

In this question, weβve been given
the coordinates of a point: negative five, two. The π₯-coordinate of the point is
negative five, and the π¦-coordinate is two. So letβs quickly recall what we
mean by saying that this point doesnβt satisfy a relation. We mean that the equation of the
relation doesnβt hold true when we substitute the value negative five for π₯ and two
for π¦. We can rephrase the question
then. Which equation or equations are not
true when π₯ is equal to negative five and π¦ is equal to two? We can just substitute the values
into each equation in turn and check whether they are true.

Firstly, five π₯ plus π¦ equals
negative 23. When π₯ is equal to negative five
and π¦ is equal to two, the left-hand side becomes five times negative five plus
two. And five times negative five is
negative 25. So weβve got negative 25 plus
two. And negative 25 plus two is
negative 23, which is equal to the right-hand side. So this equation is true. The point negative five, two does
satisfy the relation five π₯ plus π¦ equals negative 23.

How about five π₯ plus two π¦
equals zero? When π₯ is negative five and π¦ is
two, the left-hand side becomes five times negative five plus two times two. And thatβs negative 25 plus four,
which is negative 21. So substituting the value negative
five for π₯ and two for π¦ does not give an answer of zero. This point does not satisfy the
relation five π₯ plus two π¦ equals zero.

How about five π₯ plus three π¦
equals 19? We substitute the given values for
π₯ and π¦ into the equation and get negative 25 plus six, which is negative 19. The equation holds true for these
values of π₯ and π¦. So the point does satisfy this
relation.

Now, letβs look at the relation
three π₯ minus π¦ equals negative 17. We substitute π₯ equals negative
five and π¦ equals two and get negative 15 minus two, which is negative 17. So the point satisfies this
relation.

And finally the relation four π₯
plus π¦ equals negative 18. When π₯ is equal to negative five
and π¦ is equal to two, then we get negative 20 plus two, which does indeed equal
negative 18. So the equation holds true, and the
point does satisfy this relation.

So the relation that is not
satisfied by the point negative five, two is five π₯ plus two π¦ equals zero. And this is because when π₯ is
negative five and π¦ is two, as they are at the given point, then you donβt get a
result of zero when you evaluate five times π₯ plus two times π¦.