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

Given that (π‘˜, 2π‘˜) satisfies the relation π‘₯ βˆ’ 2𝑦 = βˆ’3, find the value of π‘˜.

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Video Transcript

Given that π‘˜, two π‘˜ satisfies the relation π‘₯ minus two 𝑦 equals negative three, find the value of π‘˜.

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 π‘₯ and the second coordinate is 𝑦. So therefore, in this question, we’ve got our first coordinate is π‘˜. So, that means that’s gonna be our π‘₯-coordinate. And our second coordinate is two π‘˜, so that’s gonna be our 𝑦-coordinate.

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

So therefore, what we’re gonna have is π‘˜ minus four π‘˜ equals negative three. Well, π‘˜ minus four π‘˜ is negative three π‘˜. So then, what we’ve got is negative three π‘˜ 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 π‘˜ is, well, when we do that, we’re gonna get π‘˜ 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 π‘˜, two π‘˜ satisfies the relation π‘₯ minus two 𝑦 equals negative three, then the value of π‘˜ is one.

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