Solving Systems of Equations by Elimination
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Solving systems of equations by elimination: Survivor-style. Sorry, y... the tribe as spoken.
|Algebra||Solve systems of equations|
Systems of Equations
They have thirty minutes or less to meet up, swap pizzas, and get to their correct destinations.
Julius's MathPS navigation system says the best route is four x plus three y equals seven.
Cleo's reads ten x equals six y plus four. At what point will these two drivers in the
Here are your options. We'll solve this by elimination... which is
what will happen to Julius's tip if he doesn't deliver these pizzas in time.
First, we need to put Cleo's equation into the same format as Julius's.
We do this by subtracting six-y from both sides, and we're left with ten-x minus six-y
equals four. Now, in order to eliminate a variable...
…kind of like you probably eliminate anchovies from your pizza...
We'll double all the values in Julius's equation, leaving us with eight-x plus six-y equals
fourteen. Because both equations have 6y in them, we
can add these two together to eliminate the variable y.
Eight-x plus ten-x equals eighteen-x. Six-y minus six-y eliminates that variable.
Fourteen plus four is eighteen. So we have eighteen-x equals eighteen.
Divide both sides by eighteen and we see that x equals one.
Now we'll just plug one back into the top equation.
Four times one equals four, plus three y equals seven.
Subtract four from both sides and we see that three y equals three.
Divide both sides by three, and y equals one. Looks like the answer is (1, 1), but let's
Plugging one for both x and y in the second equation checks out.
Ten minus six does, in fact, equal four. Looks like the answer is D.
So Julius and Cleo meet up at (1, 1), trade pizzas, and deliver them with minutes to spare.