Question

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

Answer 1

How did you set it up?

Answer 2

x^2+y^2=65
X-y=7

Answer 3

I substituted x for y+7 and plugged that into the X^2+y^2=65 equation.

Answer 4

Gotcha. And you solved and got y=-8 or y=1, right?

Answer 5

yup.. :/

Answer 6

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.

Answer 7

oh! i did that and i got the points (-1,-8) and (1,1).. i plugged my Y's into X-Y=7..

Answer 8

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).

Answer 9

OK, double check that point 1,1.

Answer 10

You have y =1.... and x=7 + y..... soooooooooo?

Answer 11

oh nvm. i got (8,1). I don't know what to do next. I thought those were my answers to be honest :/

Answer 12

I plug them into the orignial equation?

Answer 13

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!

Answer 14

And those are the only solutions to the system, so you know that those are ALL such numbers.

Answer 15

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...

Answer 16

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? :)

Answer 17

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.....

Answer 18

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. :)

Answer 19

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 :)

Answer 20

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! :)

Answer 21

and lol'ing at the "witchcraft".... I prefer to think of it as "mathemagic"! :)

Answer 22

Mathemagic it is!! Thank you again, have a lovely day :)

Answer 23

You too!