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ACT Math Pre-Algebra: Drill 3, Problem 4. Find the solution to this equation.
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.
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.
Full Transcript
- 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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