anonymous
  • anonymous
I keep getting this question wrong! The sum of the squares of the digits of a positive two digit number is 65. The difference between the two digits is 7. find all two-digit numbers that satisfy this statement. The correct answers are 81 and18. but i keep getting 1 and -8
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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DebbieG
  • DebbieG
How did you set it up?
anonymous
  • anonymous
x^2+y^2=65 X-y=7
anonymous
  • anonymous
I substituted x for y+7 and plugged that into the X^2+y^2=65 equation.

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More answers

DebbieG
  • DebbieG
Gotcha. And you solved and got y=-8 or y=1, right?
anonymous
  • anonymous
yup.. :/
DebbieG
  • DebbieG
Now remember what that is - it's two possible solutions FOR Y. Now you need to sub that back into the linear equation to find the X that goes with each Y.
anonymous
  • anonymous
oh! i did that and i got the points (-1,-8) and (1,1).. i plugged my Y's into X-Y=7..
DebbieG
  • DebbieG
Remember that you're solving: it's a system with a quadratic (parabola) and a linear equation (a line) so there will be, in this case, 2 solutions (that's not always true but it is here).
DebbieG
  • DebbieG
OK, double check that point 1,1.
DebbieG
  • DebbieG
You have y =1.... and x=7 + y..... soooooooooo?
anonymous
  • anonymous
oh nvm. i got (8,1). I don't know what to do next. I thought those were my answers to be honest :/
anonymous
  • anonymous
I plug them into the orignial equation?
DebbieG
  • DebbieG
OK, so you have two solutions to the system, (-1, -8) and (8, 1). I'm not sure it makes sense for the digits of a positive, 2-digt number to be negative numbers, but the solution 8, 1 certainly works. And since the requirements (sum of squares = 65 and difference of 7) don't depend on the order of the digits, then both arrangements work, e.g., 18 or 81. So those are your numbers!
DebbieG
  • DebbieG
And those are the only solutions to the system, so you know that those are ALL such numbers.
anonymous
  • anonymous
did you plug in the points we found somewhere? I'm sorry i still can't see how you ended up with 18 and 81...
DebbieG
  • DebbieG
Read the problem carefully. :) Remember what the system is modeling. The sum of the squares OF THE DIGITS of a positive two digit number is 65. The difference between THE TWO DIGITS is 7. Your x and y are DIGITS of a TWO DIGIT NUMBER. That's what all the criteria was about! So once you find the solutions for x and y, they are DIGITS of a TWO DIGIT NUMBER, so you just arrange them as such to get the number. See? :)
anonymous
  • anonymous
I'm so sorry, I'm so slow. IF i were to see this on a test, i'd probably forget this or over see it :(((( I think i understand. So in summary (from my understanding) (-1,-8) and (8,1) are my two DIGITS. therefore my answer it 18 and 81.....
DebbieG
  • DebbieG
Exactly. :) It's ok, you set up the problem correctly and it sounds to me like you basically had the solution. You were just a bit fuzzy on the interpretation, how to put that back into the question that was asked and "state the numbers" that worked. If it was a problem on one of my tests, you would get most of the credit. :)
anonymous
  • anonymous
I don't believe this is math -_- this is some sort of witchcraft! thank you for helping me and thank you for being so patient with me :)
DebbieG
  • DebbieG
The important thing is just that the "answer to the question" wasnt the solution to the system, it was to take that solution and use those as digits. :) You're welcome, happy to help and it's always nice to help someone who is working hard to understand something! :)
DebbieG
  • DebbieG
and lol'ing at the "witchcraft".... I prefer to think of it as "mathemagic"! :)
anonymous
  • anonymous
Mathemagic it is!! Thank you again, have a lovely day :)
DebbieG
  • DebbieG
You too!

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