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Solving Systems of Equations by Substitution 14325 Views


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We just love us some alliteration.

Language:
English Language

Transcript

00:04

Solving Systems of Equations by Substitution a la Shmoop

00:08

After leaving his day job as a substitute teacher… [Man walking through a school corridor]

00:11

…Mister Uboat goes to his evening job as a substitute particle physicist. [Mr Uboat in a lab coat]

00:16

Today's task at the lab is simple... solve for x and y to correctly align the particle [Two cannons labelled x and y shoot cannonballs]

00:22

cannons.

00:25

There are two equations, and x and y are the same value in each...

00:29

two-x minus three-y equals negative-two...

00:31

and...

00:32

four-x plus y equals twenty-four. [Equations written on a blackboard]

00:35

As a substitute, Mr. Uboat gets paid by the day, so he wants to get this done as efficiently [Flask bubbling]

00:39

as possible.

00:41

Let's solve this using, substitution.

00:45

The second equation looks easier to solve, so we'll start with that one. [The second equation lights up]

00:48

If we subtract four-x from both sides, we see that y equals twenty-four minus four-x.

00:54

Now we'll just substitute y for 24 minus 4x into the first equation...

00:59

to get two-x minus three, times open parenthesis, twenty-four minus four-x, closed parenthesis,

01:06

equals negative two. [The working written out on a blackboard]

01:09

Following the order of operations, we first distribute the minus 3 times the equation in the

01:14

parentheses.

01:15

Negative 3 times 24 equals 72, and negative 3 times negative 4x equals 12x, that's positive. [Finger pointing to the equation]

01:21

When we write it all out we get two-x minus seventy-two plus twelve-x equals negative

01:28

two.

01:29

Combining the x's together on the left side, we get fourteen-x minus seventy-two equals [The x's are highlighted]

01:34

negative-two.

01:36

Add seventy-two to both sides, and see that fourteen-x equals seventy.

01:40

Divide both sides by fourteen...and x equals five.

01:45

Now, remember how y equals twenty-four minus four-x?

01:50

Well, plug x as five into this equation to see what equals and you get twenty-four minus four times

01:58

five.

01:59

In other words, y equals twenty-four minus twenty, or y equals four. [Equation being solved on the blackboard]

02:06

Our answer is five, four.

02:08

Thanks to Mr. Uboat, the equation is solved!

02:11

Now the particle cannons can collide particles in peace. [The cannons fire and an explosion follows, Mr Uboat emerges with a black face and frazzled hair]

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