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

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

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

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

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

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a system of equations. And breathe.

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

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

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

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If you know how much you both started with,

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

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

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

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

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

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

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

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

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

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

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

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to get 5x equals 17 plus y.

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

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

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

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

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

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

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

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

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

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

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

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

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

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solutions, or no solution at all.

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

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you beat him at everything else.

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