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Solving Systems of Equations by Elimination a la Shmoop

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

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to the mermaid convention at the wharf...

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

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

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

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

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

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night intersect?

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

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

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

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

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

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

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

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

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can add these two together to eliminate the variable y.

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

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Boom. Gone.

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

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

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

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

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

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

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make sure.

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

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

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

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