Determining solutions to 2-variable equations and graphs
About this video
The video finds which ordered pairs are solutions to 2x + y = 8 by substituting each x and y. (3, 2) and (1, 6) make the equation true, while (5, 1) gives 11 and (2, 6) gives 10.
You'll be able to
- substitute an ordered pair into a two-variable equation.
- decide whether an ordered pair is a solution to an equation.
Key words
- ordered pair
- Two numbers written (x, y), with the x-value first and the y-value second.
- solution
- An ordered pair that makes the equation true when you substitute it.
Transcript
- [Instructor] We're told to select all ordered pairs that are solutions to the equation 2x plus y is equal to eight, and we need to pick two of these answers. So pause the video, have a go at that. All right, well, the easiest way to do this is to actually just substitute the x and the y in to see if it satisfies this equation.
So let's try out choice A. If x is five and y is one, then it would be two. Whoops, you can't see that. It would be two times five plus one. Two times five plus one is going to be 10 plus one, which is equal to 11, not eight. So I don't like that one. Let's try this one.
Two times three, now x is three. Two times, whoops. Two times three plus two is, let's see, this is six plus two, which is equal to eight. I like this one, I'll select that one. Here, we're going to have two times now in this situation, x is one, two times one plus six.
Well, that's two plus six, which is indeed equal to eight. So we are essentially done, but let's just validate this last one doesn't work. It's going to be two times this x, which is two, plus this y, which is six. This is going to be four plus six, which is 10, which indeed does not work.
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