Algebra (all content)
- Two-variable linear equations intro
- Solutions to 2-variable equations
- Worked example: solutions to 2-variable equations
- Solutions to 2-variable equations
- Completing solutions to 2-variable equations
- Complete solutions to 2-variable equations
- Solutions to 2-variable equations: substitution (old)
- Solutions to 2-variable equations: graphical (old)
An old video of Sal checking whether (3,-4) is a solution of 5x+2y=7 by graphing the equation and checking if (3,-4) is on the line. Created by Sal Khan.
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- How did you come out with 3.5?(55 votes)
- He chooses an x value and substitutes it into the equation. Using that x value, he solves for y. So,
5x + 2y = 7where x = 0 gives you the equation
5・0 + 2y = 7.
5 times 0 is 0, so simplifying the equation gives you
2y = 7.
We need to solve for y, so we divide both sides by 2.
2y / 2 = 7 / 2
2y divided by 2 is just
7 divided by 2 is
Therefore, the final equation is
y = 3.5.
Hope that helps! :)(102 votes)
- We just started this subject in math today. The teacher explained the process to us and I didn't really understand it. I just watched the viedo and I still don't understand it. Could you explain it to me plz? thank you! =)(10 votes)
- How does drawing the line on the graph prove that 3,-4 are the solution to 5x+2y=7?(6 votes)
- The line is the line of the equation 5x+2y=7. If (3,-4) co-ordinate falls on that line, then it is a solution of the equation.(2 votes)
- Would (2, -5) be a solution to 4 + 3x = -2y? When Sal does the equations like the one in this video I am able to understand it, but when the y value is to the right of the equal sign, I am not sure how to do it correctly.(2 votes)
- The equation is no different when the y is on the right side of the equation. If you are not understanding the equation while it is in this form, you can flip the equation so y is on the left side. Hope this helps you get the correct answer for the equation.(2 votes)
- What is the purpose for graphs when you have equations?(2 votes)
- How do you tell that 5+2y=7. Then 2y=2, then y=1?(1 vote)
- You just answered your own question... I think? y=1, therefore, if you substitute y for 1 in "5+2y=7", it would be the same as saying 5+2x1=7. Usually, variables or unknown numbers are represented by letters (ie. x, y, n, etc.) In this case, you already told me that y=1 and so you would put in a 1 wherever the y appears.(3 votes)
- i keep failing my math class i need help(2 votes)
- get a tutor or ask someone you know that is good at math help you or join a class on khanacademy or get a coach(1 vote)
Is 3 comma negative 4 a solution to the equation 5x plus 2y is equal to 7? So there's two ways to think about it. One, you could just substitute this x and y value into this equation to see if it satisfies-- and then we'll do that way first-- and the other way is if you had a graph of this equation, you could see if this point sits on that graph, which would also mean that it is a solution to this equation. So let's do it the first way. So we have 5x plus 2y is equal to 7, so let's substitute. Instead of x, let us put in 3 for x. So 5 times 3 plus 2 times y-- so y is negative 4-- plus 2 times negative 4 needs to be equal to 7. I'll put a question mark here, because we're not sure yet if it does. So 5 times 3 is 15, and then 2 times negative 4 is negative 8. So the left hand side, it simplifies to 15 minus 8, and this needs to be equal to 7. And of course, 15 minus 8 does equal 7, so this all works out. This is a solution, so we've answered the question. But I also want to show you, this way we just did it by substitution. If we had the graph of this equation, we could also do it graphically. So let's give ourselves the graph of this equation, and I'll do that by setting up a table. There's multiple ways to graph this. You could put it in a slope-intercept form and all of the rest, but I'll just set up a table of x and y values. And I'll graph it, and then given the graph, I want to see if this actually sits on it. And obviously it will, because we've already shown that this works. In fact, we could try the point 3, negative 4, and that actually is on the graph. We could do it on our table, but I won't do that just yet. I'm just going to do this to give ourselves a graph. So let's try it when x is equal to 0. We have 5 times 0 plus 2 times y is equal to 7. So when x is equal to 0, y is going to be-- so you're going to have 0 plus 2y is equal to 7. y is going to be equal to 3.5. When x is equal to 1, you have 5 plus 2y is equal to 7. If you subtract 5 from both sides, you get 2y is equal to 2. You get y is equal to 1. So when x is 1, y is 1, and when x is-- well let's try-- well that's actually enough for us to graph. We could keep doing more points. We could even put the point 3, negative 4 there, but let's just try to graph it in this very rough sense right here. So let me draw my x-axis, and then this right over here is my y-axis. And let me draw some points here. So let's say that this is y is 1, 2, 3, 4. This is negative 1, negative 2, negative 3, negative 4. I could keep going down in that direction. This is 1. Let me do it a little bit-- 1, 2, 3, 4, and I could just keep going on and on in the positive x direction. So let's plot these points. I have 0, 3.5. When x is 0, y is 1, 2, 3.5. When x is 1, y is 1. And so if we were to draw this line-- I'll do it as a dotted line, just so that I can make sure I connect the dots. I can do a better job than that though. So it will look something like that. And so if someone gave you this line, you'd say oh, well it's 3, negative 4 on this line, and let's assume that we drew it really nicely and this was all to scale. Let me try one last attempt at it. So it's going to look something like that. And If someone asked is 3, negative 4 on it, you could visually do it, but it's always hard when you actually don't substitute it, because you don't know. Maybe you're a little bit off. But if you look at it over here, you say when x is equal to 3, what is y? Well, you go down here, and it looks like y is equal to negative 4. So this is a point 3 comma negative 4. Obviously, in general, you don't want to just rely off of inspecting graphs. Maybe this was 3, negative 3.9999, and you just couldn't tell looking at the graph. That's why you always want to just the substitute and make sure that it really does equal, that this equality really does hold true at that point, not just looking at the graph. But it's important to realize that the graph really is another representation to all of the solutions of this equation.