Question

What are the coordinates to the solution that lays in quadrant 1?
x^2-y^2=25
x+y=25

Answer 1

All coordinates in quadrant 1 are positive

Answer 2

good to know

Answer 3

I tried squaring the second equation and then adding both equations together, which essentially canceled out the y^2's so then I solved for x but came up with an odd number.

Answer 4

\(x^2-y^2=(x-y)(x+y)=25\)
now use the second equation
x+y=25
hope this is enough, :)

Answer 5

thanks for that but what do I do with that information?

Answer 6

next step would be:
x-y=1
x+y=25

Answer 7

then
2x=26
x=13
y=12

Answer 8

so you basically took the square root of the top equation

Answer 9

i used the fact that
a^2-b^2=(a-b)(a+b)

Answer 10

how did 25 go to 1?

Answer 11

if in
(x-y)(x+y)=25
you substitute the value of (x+y) from second equation, you get
(x-y)25=25
or
x-y=1

Answer 12

got it?

Answer 13

okay

Answer 14

Nice solution. Another way to do it is solve for x in the second equation and substitute it in the first equation. That gives you a quadratic and more work involved to get the answer.

Answer 15

Yeah I figured it out though:) (13,12)