Question Video: Finding the Unknown in a Problem Involving a Point Satisfying a Given Relation Mathematics • Second Year of Preparatory School

Video Transcript

Given that the ordered pair 𝑘, two 𝑘 satisfies the relation 𝑥 minus two 𝑦 equals negative three, find the value of 𝑘.

In this example, we’re given the equation of a relation 𝑥 minus two 𝑦 equals negative three. We note first that this is a linear relation since each of the two variables 𝑥 and 𝑦 occur only to the power one. And we define a linear relation such that if two variables 𝑥 and 𝑦 are related by an equation of the form 𝑎𝑥 plus 𝑏𝑦 equals 𝑐 for constants 𝑎, 𝑏, and 𝑐, then 𝑥 and 𝑦 are linearly related.

We recall also that such a relation can be represented by a set of ordered pairs 𝑥, 𝑦. Now we’re given a particular ordered pair that satisfies the relation 𝑥 minus two 𝑦 equals negative three. That’s the ordered pair 𝑘, two 𝑘 so that together the values 𝑥 equals 𝑘 and 𝑦 equals two 𝑘 satisfy the given equation.

And we need to find the value of 𝑘. We can do this by substituting our 𝑥- and 𝑦-values into the equation and solving for 𝑘. This gives us 𝑘 minus two multiplied by two 𝑘 is equal to negative three. That’s 𝑘 minus four 𝑘 equals negative three. And since 𝑘 minus four 𝑘 is negative three 𝑘, we have negative three 𝑘 equals negative three. If we then divide both sides by negative three, we have 𝑘 equal to positive one.

Hence, if the ordered pair 𝑘, two 𝑘 satisfies the relation 𝑥 minus two 𝑦 equals negative three, then 𝑘 is equal to one.