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x + 2y = 3 dan x + 3y = 4

Alright, we're given two equations and the only thing I can assume is that we wanted to solve this what's called a system of equations solve for X and solve for Y. We have a couple of different ways of solving systems of equations. We can do it by graphing by substitution and by elimination, those are the three most common ways of solving systems of linear equations. Um In this case I think it really lends itself to elimination because I already have one X and one X. All I'm going to do is actually subtract my two equations. So I'm going to subtract these two from each other. Alright. Make sure you're careful when you do that, it's X minus X. Which is going to be zero X. So that's why we do this to get rid of that. But now I have two y minus three Y. Two Y minus three Y. It leaves me with a negative Y. And that's equal to and now I have my 3 -43 -4 is negative one. All right now I don't want a negative Y. So I'm going to divide by negative ones. I have to divide the other side by negative one as well and I'm left with positive Y. Is equal to positive one. So there's one of my two variables now to figure out what the other one is. You take it and you substitute it into either of the two original equations. I'll just substitute it in right here. So I get X plus two times my Y value which we just said was one Is equal to three. Alright well that's just X plus two is equal to three. I'm going to subtract the two from both sides and of course I get X equals one as well. So actually both X and Y have the same value in this problem. X equals one. Y equals one. It's always a good idea to check it in the second equation. In other words I have substituted in here and found that X equals one. Now I'm going to go back to my second equation and substitute and make sure it works. So X is one so it becomes one plus three times my Y value which was also one is equal to four. And that's pretty easy to check. One plus three equals four. And sure enough when we add them we do get four. So your answers are both X and Y equal one.

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Lectures

01:32

In mathematics, the absolute value or modulus |x| of a real number x is its numerical value without regard to its sign. The absolute value of a number may be thought of as its distance from zero along a number line; this interpretation is analogous to the distance function assigned to a real number in the real number system. For example, the absolute value of ?4 is 4, and the absolute value of 4 is 4, both without regard to sign.

01:11

04:10

$$y-3 x+(4 y+3 x) \frac{\mathrm{d} y}{\mathrm{~d} x}=0$$

01:04

$$y=3 x+4$$

00:33

$$3 x+y=-2$$

00:26

02:12

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