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Introduction to Systems of Equations 8626 Views


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Transcript

00:08

All right, we know you're so in love with equations, that you're gonna be...

00:12

thrilled to learn that there are whole systems of them. Before you start crying...

00:16

into your algebra textbook, they're really much more harmless than they sound. In fact,

00:20

if you have one equation with variables, and then at least one other...

00:24

equation with the same variables, well, that's it. You've got yourself...

00:28

a system of equations. And breathe.

00:35

These can be used to compare any two or more things that have stuff in common.

00:41

Like, if you wanted to compare your savings account with your little brother's...

00:45

savings account to see who's a better...saver.

00:50

If you know how much you both started with,

00:54

and the rate at which you're both saving, or compounding your investments, you can determine whether he'll...

00:59

ever have as much money in his account as you do. And if not,

01:02

you'll be able to lord the fact over him for all eternity.

01:04

Man, you guys are competitive. Say we've got two linear equations,

01:12

All we'd need to do to solve this system of equations, is...

01:15

to find a value of x and a value of y, which will make both...

01:19

of these equations true. That is, for whatever x's you have over...

01:23

here, or whatever y's you have, they're gonna produce the same...

01:26

answer over here. Well the simplest way is to try to get one of the variables...

01:30

all by its lonesome. Well, here the y term in the second equation...

01:34

is already by itself, so let's start there. We can add y to both sides...

01:38

to get 5x equals 17 plus y.

01:42

Then subtract 17 from both sides, to get 5x minus 17 equals y.

01:49

From there we can take the quantity "5x minus 17" and plug it into the y...

01:53

term in the first equation. That gives us 3x plus 2, times the quantity...

01:59

"5x minus 17" equals 18. Well, distribute the...

02:03

2 and it simplifies to 3x plus 10x minus 34 equals 18. Well our...

02:09

3x and 10x total 13x, and if we add 34 to both sides...

02:13

we get 13x equals 52. Divide both sides 13, and x equals, yep, 4.

02:19

Nice easy number. So we can plug into the x term in either equation to get the value of the y term.

02:25

Well 3 times 4 plus 2y equals 18, so 12 plus 2y equals 18.

02:32

So subtract 12 from both sides, then 2y equals 6. Divide both...

02:37

sides by 2, and y equals, yep, 3. Just like that, we've solved our system of equations.

02:42

And once you get the hang of these puppies, you can graph 'em. Yeah, just like this.

02:47

And that way you can determine if there's a single solution, infinite...

02:51

solutions, or no solution at all.

02:55

Well, in the case of your little brother, the best solution might be to let him have this one. Goodness knows...

03:00

you beat him at everything else.

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