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### Course: Algebra (all content) > Unit 5

Lesson 2: Introduction to systems of equations- Systems of equations: trolls, tolls (1 of 2)
- Testing a solution to a system of equations
- Solutions of systems of equations
- Systems of equations: trolls, tolls (2 of 2)
- Systems of equations with graphing: y=7/5x-5 & y=3/5x-1
- Systems of equations with graphing: exact & approximate solutions
- Systems of equations with graphing

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# Systems of equations with graphing: y=7/5x-5 & y=3/5x-1

Sal graphs the following system of equations and solves it by looking for the intersection point: y=7/5x-5 and y=3/5x-1. Created by Sal Khan.

## Want to join the conversation?

- What do you mean when you say "when x is equal zero, y is equal to negative 5," That did not make sense to me. i could be because of the way I explain things when i grph but it did not make sense to me.(41 votes)
- He meant that the y-intercept of that equation is -5. At the y-intercept, x=0 and y=-5 for this equation.(20 votes)

- I'm sooo confused.

How exactly do you plot it?(26 votes)- you take the y intercept and plot it on the y-axis then use the slope (example:4x or 2/3x) if its 4 then go four up and if its -4 go four down if its a fraction like 3/5 then use rise over run and go up 3 and over 5(6 votes)

**i thought you move 3 to the right and 5 up for the equation's rise over run**(10 votes)- Yes, the slope means rise over run. It doesn't make sense for Rise to mean go right. Think of the meaning of the word. Rise means go up. So, Rise = up/down and Run = left/right.

Hope this helps.(20 votes)

- what if it is just a whole number, not a fraction(10 votes)
- Since we can divide by 1 and not change the value, 5 becomes 5/1.(14 votes)

- So, how would you plot something like

7x−y=7

x+2y=6

I cannot figure out how to plot it.(6 votes)- Hi Amberlynn,

Great question!

If you don't know yet, there's something called "isolating the variable". It's getting a variable on one side of an equation with everything else on the other side. In this case, you want y to be isolated. Let's go:

7x - y = 7

You want to subtract 7x from both sides to get the x value on the right:

7x - y = 7

-7x - y = 7 - 7x

7x - 7x = 0x so you get:

-y = 7 - 7x

You need to have the y positive, so multiply everything by it's opposite.

(+)-y = (-)+7 (+)-7x

The parts in the parenthesis are what's added to the original equation to make the y positive. So here's your answer:

y = -7 + 7x

Now for your next one:

x + 2y = 6

You want to have the "x" on the right. You'll need to add a negative x to each side to subtract out the "x" on the left because a positive x + a negative x equals 0.

x + 2y = 6

-x + 2y = 6 - x

Notice that I don't make the right side of the equation have a positive x. Then you divide each term by two because you want to have the y by itself.

x + 2y = 6

-x + 2y = 6 - x

2y/2 = 6/2 - x/2

y = 3 - (1/2)x

Time to graph them!

Hope this helped, and good luck on your math!(15 votes)

- I got lost instantly.(11 votes)
- What we're doing here is graphing out a line based on this equation. First we can find the y-intercept (the point where the line crosses the x axis). Since the y axis is naturally at x = 0, we can plug x into the equation and then solve for y. In the first equation in this video, that would be y=0-5. Now that very obviously means that one point on this line is 0,5. Then, since we know the slope is 7/5 (y=mx+b, remember?) we can find another point by "rising" 7 and "running" 5. That means we get another point we can use to graph the line, in this case 5,12. Then, you do the exact same thing to graph the second line and the intersection is the solution to this problem. I know this is late but I hope it helps anyone who is struggling.(1 vote)

- What is the troll he's talking about in0:02?(4 votes)
- Watch the 2 previous videos Sal has made in that catagory. Hope that helps!(5 votes)

- I sometimes still have a hard time finding the slope. On :36 it says the Y intercept is equal to 5. Does that mean that the -5 is the Y intercept. If so than the number without the variable is always the Y intercept?(4 votes)
- the y intercept is -5 is correct. Since it is where x = 0, no matter what the slope is, if I multiply by 0 I will always get zero.(3 votes)

- I'm really confused how he did it because all i saw him do was move around the dots. Can someone please help me?(0 votes)
- Yeah, that's pretty much it for this exercise: moving around dots, but the "math" part is the line that's connected to the dots. You're basically "drawing" a line by moving the dots. I'll see if I can explain it a different way to make it easier to understand.

y = x

This one's pretty simple to graph. It's just a diagonal line where at any point it's the same distance from the x axis as it is from the y axis.*(I really wish I could show you graphs in these answers but I don't think I can. Sadness)*All the other equations we'll talk about will look like this one, but changed a little bit.

Let's try another.

y = x + 1

This is just like the other one, but it's shifted up one unit. If**x = 1**, then**y = 1 + 1**or**2**. If**x = 7**then**y = 7 + 1**which is**8**.

y = x + 4

This one's the same as the other one, but shifted up 4 units.

Now let's change the*slope*of the line.

y = 2x

Now the line is steeper. If**x = 1**then**y = 1*2**or**2**If**x = 5**then**y = 5*2**or**10**

y = ½x

This one's like the other one, except instead of the line being steeper, it's less steep. Instead of multiplying by 2, we divide by 2. If**x = 1**then**y = 1/2**. If**x = 8**then**y = 8/2**which equals**4**

Okay, let's do one last one.

y = 3x + 2

In this one, we have to shift it up, and make it steeper. If**x = 1**then**y = 1*3 + 2**which equals**5**. If**x = 7**then**y = 7*3 +2**which is*(seven times three is 21, plus 2...)***23**

I don't know if this was helpful*at all*but this concept is really hard to explain without being able to draw. Please let me know if this helped, or if you have any further questions. :)(11 votes)

- I'm having trouble locating what he's doing and where his mouse is. 😕(5 votes)

## Video transcript

Just in case we encounter
any more trolls who want us to figure out
what types of money they have in their pockets,
we have devised an exercise for you to practice with. And this is to solve systems
of equations visually. So they say right over here,
graph this system of equations and solve. And they give us two equations. This first one in blue, y
is equal to 7/5x minus 5, and then this one in green,
y is equal to 3/5x minus 1. So let's graph each
of these, and we'll do it in the
corresponding color. So first let's graph
this first equation. So the first thing I see is
its y-intercept is negative 5. Or another way to think about
it, when x is equal to 0, y is going to be negative 5. So let's try this out. So when x is equal
to 0, y is going to be equal to negative 5. So that makes sense. And then we see
its slope is 7/5. This was conveniently placed
in slope-intercept form for us. So it's rise over run. So for every time it moves
5 to the right it's, going to move seven up. So if it moves 1, 2,
3, 4, 5 to the right, it's going to move 7 up. 1, 2, 3, 4, 5, 6, 7. So it'll get right over there. Another way you could
have done it is you could have just tested
out some values. You could have said, oh,
when x is equal to 0, y is equal to negative 5. When x is equal to 5, 7/5
times 5 is 7 minus 5 is 2. So I think we've properly
graphed this top one. Let's try this bottom
one right over here. So we have when x is equal to
0, y is equal to negative 1. So when x is equal to 0,
y is equal to negative 1. And the slope is 3/5. So if we move over 5 to the
right, we will move up 3. So we will go right
over there, and it looks like they intersect
right at that point, right at the point x is
equal to 5, y is equal to 2. So we'll type in x is equal
to 5, y is equal to 2. And you could even verify
by substituting those values into both equations,
to show that it does satisfy both constraints. So let's check our answer. And it worked.