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Problem 2 Hard Difficulty

$$\begin{array}{c}{x+y=0} \\ {3 x-2 y=10}\end{array}$$
Which of the following ordered pairs $(x, y)$ satisfies
the system of equations above?
$$\begin{array}{l}{\text { A) }(3,-2)} \\ {\text { B) }(2,-2)} \\ {\text { C) }(-2,2)} \\ {\text { D) }(-2,-2)}\end{array}$$

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Video Transcript

Hey, so this one says What do the following order? Paris have a system of equations above? Well, if we have assistance of equations, that means that we have to solve it by combining them. Once we combine them, we can isolate the X and the Y. So in order to do that, I'm going to go ahead and multiply. This choppy question by two is if I'm not by the entire thing by two, and I get two X Plus two y is equal to zero. And then now it allows me to add the two equations if I have to expose to eyes equal to zero and three X minus two, eyes equal to ten. If I add them, then you can notice that this positive line the negative to whack and cancel out. So then to expose three Axis five x on this Europe list Tennis ten. So then, finally, to isolate our ex, I'm just going to subtract or divide both sides by five. Leaving me with the X is equal to two, so from there, we already know that are correct. Answer has to be because that's the only one with a two positive to as our ex Cordant. But let's go and try playing it back into the original just to make sure. So if I do that, I get to plus some, why is equal to zero and that three terms to minus some? Why is equal to ten? Well, for this one, if we subtract two from both sides, we get that Y is equal to negative twos. That one works for the bottom one. We have six minus two. Y is equal to ten, and then if we plug in a negative to their six minus two times, negative, too, is, in fact equal to turn, so we know that B works.