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Problem 8

In Exercises 7 - 10, determine whether each …


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Problem 7

In Exercises 7 - 10, determine whether each ordered pair is a solution of the system of equations

$ \left\{\begin{array}{l} 2x - y = 4\\8x + y = -9\end{array}\right. $

(a) $ (0 , -4) $
(b) $ (-2 , 7) $
(c) $ (\dfrac{3}{2} , -1) $
(d) $ (- \dfrac{1}{2} , -5) $


a) $(D)(-1 / 2,-5)$
b) $(D)(-1 / 2,-5)$
c) $(D)(-1 / 2,-5)$
d) $(D)(-1 / 2,-5)$



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Video Transcript

Okay, So for this problem, we have two equations. We have two x minus y equals four. We have eight x plus. Why equals negative? Nine. And what this problem is asking us to do is to take the four points. I'm just playing the man and see if they work. That means each point has an X and y value was compliant breaks. And why? And see if they give us for it if they give us negative nine. So let's just start with a We're only if, If there's an answer, we're only going to have one answer. Let's keep going on. So, uh, point a is zero negative for So if I plug in zero negative for have to time zero, uh minus No, I get it for which is just that's a dumb 00 It's attract negative for really just adding for which does equal are four first equation works for a second equation. We're gonna do eight times zero on negative for eight times 00 for your adding negative four to same subtracting for that's negative. Four, which is not negative. Nine. So for incestuous, eh? This will not work and Citrus be we have. We're playing a negative two in seven. So you have two times two minus two times two is four four minus seven snail or three, which is not for so we can stop there because it has to work for both equations. That's a and B says, create a new son and talk about CND. The answer to a C was three halves, a negative one. So for playing that end, we have two times three halves minus negative one. I'm trying to see if that equals four in two times. Three. House just three three minus negative one. That's just three plus one. And does he Before first equation for a second equation, we're going to eight times three over two. Plus, you know you're not blind. We're trying to see if that's gonna equal negative time. Eight times three over two is just 12 for adding negative ones. That same subtracting one just just so 11 which does not equal negative nine. So answer choice, see, is also wrong. So going for answer choice d, we have negative 1/2 negative five case that appointment, and we're going to times negative one hand when it's attract negative fun receipt that equals four. So two times native, 1/2 his native one we subtract Negative five Seems adding fine. Negative one plus five Does evil for this is the first equation is correct. Second equation, we have eight times negative. 1/2 plus negative five. We're trying to see if that's gonna equal. Now, eight times a night of 1/2 is negative. For for adding negative finds, Seamus attracting by this does equal negative nine. We were looking for negative nine. And so we have two equations of that work. This point works in both equations. Two. This answer choice D is our only one network since And we should only have one answer that does work, if any at all. So answer choice D ding, ding, ding. That is our answer for this problem. It works when you plug it into both equations. Thank you very much.

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