Video: Determining Which Linear Equation a Given Point Does Not Satisfy

Which of the following relations does the point (−5 ,2) not satisfy? [A] 5𝑥 + 2𝑦 = 0 [B] 4𝑥 + 𝑦 = −18 [C] 3𝑥 − 𝑦 = −17 [D] 5𝑥 + 3𝑦 = −19 [E] 5𝑥 + 𝑦 = −23

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Video Transcript

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

So, the first thing we’re gonna do is look at our point. And the point is negative five, two. So, we’ve got an 𝑥-value of negative five, so that’s our 𝑥-coordinate, and a 𝑦-value of two. So, if we want these relations to be satisfied by this point, then what that means is if we substitute in 𝑥 equals negative five and 𝑦 equals two, then the equation should work.

So, I’m gonna evaluate them each in turn and we start with our first equation, A. So, if we substitute in our values for 𝑥 and 𝑦, we’re gonna get five multiplied by negative five plus two multiplied by two. And this is gonna give us negative 25 plus four, which will be equal to negative 21. And that’s because if we’re adding four to negative 25, it means we’re going up a number line. So, we’re going to the right. So therefore, it’s gonna become less negative by four, which gives us the answer negative 21.

Well, this clearly isn’t equal to the value we’re given in the equation, and that is zero. So therefore, we could say that the point negative five, two does not satisfy this equation. So, this looks like it’s going to be the answer, but we’ll double check with the others just to make sure.

Well, for B, we have four multiplied by negative five plus two, which gives us negative 20 add two. So again, we are adding to a negative. Therefore, it becomes less negative, which means we go to the right up our number line, which means we get negative 20 plus two is equal to negative 18. And this is the value we expected. So, we can say that the point negative five, two does satisfy this relationship or equation.

Now, let’s move on to C. Well, for C, we’re gonna have three multiplied by negative five minus two. This is equal to negative 15 minus two, which gives us negative 17, which matches the value that we had for C. So therefore then, we can say that this is satisfied by the point negative five, two. So now, let’s move on to D. Well, for D, we have five multiplied by negative five plus three multiplied by two, which gives us negative 25 plus six, which gives us negative 19. So therefore, this matches what we expected for D. So, we can say that this has been satisfied by the point negative five, two.

One more left, which is E. And for E, we’ve got five multiplied by negative five plus two, which is gonna be equal to negative 25 add two, which gives the result negative 23. So therefore again, E is satisfied by the point negative five, two.

So now, I’ve gotta look at what we wanted for the question. Well, the question wants to know which of the following relations the point negative five, two does not satisfy. Well, that’s A cause we showed that that wasn’t satisfied by the point negative five, two because the result should’ve been zero and we found that it would’ve been negative 21. So therefore, we can say the correct answer is A.

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