Question Video: Determining Which Linear Relation a Given Point Does Not Satisfy Mathematics • Second Year of Preparatory School

Video Transcript

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

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

Firstly, five 𝑥 plus 𝑦 equals negative 23. When 𝑥 is equal to negative five and 𝑦 is equal to two, the left-hand side becomes five times negative five plus two. And five times negative five is negative 25. So we’ve 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 𝑥 plus 𝑦 equals negative 23.

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

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

Now, let’s look at the relation three 𝑥 minus 𝑦 equals negative 17. We substitute 𝑥 equals negative five and 𝑦 equals two and get negative 15 minus two, which is negative 17. So the point satisfies this relation.

And finally the relation four 𝑥 plus 𝑦 equals negative 18. When 𝑥 is equal to negative five and 𝑦 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 𝑥 plus two 𝑦 equals zero. And this is because when 𝑥 is negative five and 𝑦 is two, as they are at the given point, then you don’t get a result of zero when you evaluate five times 𝑥 plus two times 𝑦.