Question

In the system shown below, what are the coordinates of the solution that lies in quadrant I?

Write your answer in the form (a,b) without using spaces.


x^2-y^2=25
x+y=25

Answer 1

First solve one of the equations for one variable. Since both equations have y^2 in them, we'll solve the bottom for y^2:

x - y^2 = -5
-y^2 = -x - 5
y^2 = x + 5

Substitute this for y^2 in the first equation:

x^2 + (x + 5) = 25
x^2 + x - 20 = 0

Now factor:
(x + 5)(x - 4) = 0
x = -5 or x = 4
Since the point is in Quadrant I, we know x has to be positive, so x=4

Now to get y, plug x into one of the equations:

x - y^2 = -5
4 - y^2 = -5
-y^2 = -9
y = 3

Your point is (4,3)

Hope this helps :-)

Answer 2

\[x^2-y^2=25\]
\[(x+y)(x-y)=25\]
\[x+y=25\]
\[x-y=1\] add to get
\[2x=26\]
\[x=13\] then solve for y

Answer 3

answer is (13,12)
(4,3) does not work because 4 + 3 = 7, not 25