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Solving Systems of Equations by Elimination 8201 Views


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Description:

Solving systems of equations by elimination: Survivor -style. Sorry, y ... the tribe as spoken.

Language:
English Language

Transcript

00:05

Solving Systems of Equations by Elimination a la Shmoop

00:12

Julius the pizza delivery driver is taking a huge order of one hundred anchovy pizzas

00:16

to the mermaid convention at the wharf...

00:18

…when he discovers that his one hundred pizzas somehow got mixed up with Cleo's hundred

00:29

pepperoni pizzas she was supposed to be driving to the national cheerleading tryouts.

00:39

They have thirty minutes or less to meet up, swap pizzas, and get to their correct destinations.

00:45

Julius's MathPS navigation system says the best route is four x plus three y equals seven.

00:52

Cleo's reads ten x equals six y plus four. At what point will these two drivers in the

01:00

night intersect?

01:01

Here are your options. We'll solve this by elimination... which is

01:13

what will happen to Julius's tip if he doesn't deliver these pizzas in time.

01:17

First, we need to put Cleo's equation into the same format as Julius's.

01:22

We do this by subtracting six-y from both sides, and we're left with ten-x minus six-y

01:28

equals four. Now, in order to eliminate a variable...

01:32

…kind of like you probably eliminate anchovies from your pizza...

01:36

We'll double all the values in Julius's equation, leaving us with eight-x plus six-y equals

01:41

fourteen. Because both equations have 6y in them, we

01:45

can add these two together to eliminate the variable y.

01:48

Eight-x plus ten-x equals eighteen-x. Six-y minus six-y eliminates that variable.

01:56

Boom. Gone.

01:58

Fourteen plus four is eighteen. So we have eighteen-x equals eighteen.

02:03

Divide both sides by eighteen and we see that x equals one.

02:09

Now we'll just plug one back into the top equation.

02:12

Four times one equals four, plus three y equals seven.

02:16

Subtract four from both sides and we see that three y equals three.

02:19

Divide both sides by three, and y equals one. Looks like the answer is (1, 1), but let's

02:25

make sure.

02:27

Plugging one for both x and y in the second equation checks out.

02:32

Ten minus six does, in fact, equal four. Looks like the answer is D.

02:38

So Julius and Cleo meet up at (1, 1), trade pizzas, and deliver them with minutes to spare.

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