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### Course: Algebra (all content) > Unit 3

Lesson 1: Two-variable linear equations intro- 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)

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# 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.

## Want to join the conversation?

- 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 = 7`

where x = 0 gives you the equation`5・0 + 2y = 7`

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5 times 0 is 0, so simplifying the equation gives you`2y = 7`

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We need to solve for y, so we divide both sides by 2.`2y / 2 = 7 / 2`

2y divided by 2 is just`y`

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7 divided by 2 is`3.5`

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Therefore, the final equation is`y = 3.5`

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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)
- All you are doing is replacing x and y with their respective values and solving it.(5 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)

- ordered pair solutions for x=0(4 votes)
- what is 2x-8y=8(4 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)

- is -4,5 a solution of y =2x-4(2 votes)
- What is the purpose for graphs when you have equations?(2 votes)
- i think it is so the teachers can see if u understand the problem(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)

## Video transcript

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.