Question Video: Finding the Unknown in a Problem Involving a Point Satisfying a Given Relation Mathematics • 8th Grade

Video Transcript

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

So when we take a look at any pair of coordinates, what we can always say is that the first number or first coordinate is 𝑥 and the second coordinate is 𝑦. So therefore, in this question, we’ve got our first coordinate is 𝑘. So, that means that’s gonna be our 𝑥-coordinate. And our second coordinate is two 𝑘, so that’s gonna be our 𝑦-coordinate.

So we’re told in this question that the coordinate pair 𝑘, two 𝑘 satisfies the relation 𝑥 minus two 𝑦 equals negative three. So therefore, to solve, what we can do is substitute or sub 𝑥 equals 𝑘 and 𝑦 equals two 𝑘 into our equation, which is 𝑥 minus two 𝑦 equals negative three. And when we do that, what we’re gonna get is 𝑘, and that’s because that was our 𝑥, minus and then we’ve got two multiplied by two 𝑘. And that’s cause we had two 𝑦 and 𝑦 equals two 𝑘. And then this is equal to negative three.

So therefore, what we’re gonna have is 𝑘 minus four 𝑘 equals negative three. Well, 𝑘 minus four 𝑘 is negative three 𝑘. So then, what we’ve got is negative three 𝑘 equals negative three. So then, if we divide both sides of the equation by negative three, and we want to do that cause we want to find out what single 𝑘 is, well, when we do that, we’re gonna get 𝑘 is equal to one. And that’s because if we divide negative three by negative three, this is just one.

So, we can say that given that 𝑘, two 𝑘 satisfies the relation 𝑥 minus two 𝑦 equals negative three, then the value of 𝑘 is one.