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How did you set it up?
I substituted x for y+7 and plugged that into the X^2+y^2=65 equation.
Gotcha. And you solved and got y=-8 or y=1, right?
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.
oh! i did that and i got the points (-1,-8) and (1,1).. i plugged my Y's into X-Y=7..
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).
OK, double check that point 1,1.
You have y =1.... and x=7 + y..... soooooooooo?
oh nvm. i got (8,1). I don't know what to do next. I thought those were my answers to be honest :/
I plug them into the orignial equation?
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!
And those are the only solutions to the system, so you know that those are ALL such numbers.
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...
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? :)
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.....
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. :)
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 :)
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! :)
and lol'ing at the "witchcraft".... I prefer to think of it as "mathemagic"! :)
Mathemagic it is!! Thank you again, have a lovely day :)