Solve each problem. See Examples 5 and 9. The sum of two numbers ...

Question

Solve each problem. See Examples 5 and 9. The sum of two numbers is 47, and the difference between the numbers is 1. Find the numbers.

Accepted Answer

Hello, everybody. I, I, today, today we're going to be looking at this question that states find two numbers that sum up to 195 and have a difference of three. And the extras provided are a 99 and 96 B 99 98 95. C 195 and D 94. Now, the first thing I'll do is I'll assign variables to my numbers. So we have that two numbers sum up to X to 1 95. So that's the same thing as saying that X plus Y is equal to 195 where X could be one number and Y could be the other number. And we'll call that equation number one. Now, right under that equation, I'm going to write equation number two, which will be the difference. So we have the difference of the two numbers will be three. So X minus Y equals three and I write them one on top of the other, the equations because we're going to be using a method called elimination where we add up both of our equations. And when we're adding, usually when we add numbers, we are taught to put them one on top of the other and you draw the line and draw the addition symbol and just add them up. So we do the same thing with our equations here. We have X plus Y equals 195 on top. And we're adding that with X minus Y equals three on the bottom. So we'll go one by one. So we have that X plus X will be two X and then we have part one, Y minus Y. And this is why it's called elimination because we are eliminating the Y if we have one, Y minus Y and we have zero Y and we eliminate the Y variable and then we have 195 plus three is 198. So we have that two, X is equal to 198. So to isolate the X, now we divide both sides by two and we'll have that X is equal to 99 and that'll be our first number. Now, we can use that to plug that back into one of our equations. In this case, I'll use equation number two. But you can use either equation and you, all, you have to do is plug in the X that we now know. So in equation number two, we had X minus Y equals three. So now we have 99 minus Y equals three, which means that Y is equal to 96. And that'll be our second number, meaning that our two numbers will be 99 96 or answer choice. A so I hope that was helpful and until next time.

Solve each problem. See Examples 5 and 9. The sum of two numbers is 47, and the difference between the numbers is 1. Find the numbers.

Key Concepts

Systems of Equations

Linear Equations

Algebraic Manipulation

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