Solve the system : x + y = 5 x^2 + y^2 = 13

To solve the sytem of
equations:

x+y = 5 ..........(1)
and 

x^2+y^2 = 13......(2).

We we
know   2xy = (x+y)^2 - (x^2+y^2).

Therefore 2xy = 5^2-13 = 25-13 =
12.

Therefore (x-y)^2 = x^2+y^2-2xy = 13 -12 =
1.

Therefore  x-y = sqrt {(x-y)^2 } =  sqrt1 or
-sqrt1.

 x-y = 1. Or x-y = -1.

Or x-y =
1....(3).

x+5 =
5........(1).

(1)+(3):

2x = 1+5=
6.

x = 6/2 =
3.

(1)-(3):

2y = 5-1 =
4.

 y = 4/2 = 2.

Therefore the solution
of the system of equations: x= 3, y = 2,
O

Or 

By using the equations x-y =
-sqrt1 = -1, x+y = 5, we get x = 2 and y = 3.