If x^2 + y^2 = 29 and x+ y = 7 Then find x and y.

Given the equations:

x^2 +
y^2 = 29..............(1)

x+ y =
7.......................(2)

We have a system of two
equations and two variables. Then, we can use the substitution or the elimination method
to solve.

Let us use the substitution method to
solve.

We will re-write equation
(2).

x+ y = 7

==> y = 7
- x

Now we will substitute in
(1).

x^2 + y^2 = 29

==>
x^2 + ( 7-x)^2 = 29

==> x^2 + 49 - 14x + x^2 =
29

==> 2x^2 - 14x + 49 - 29 =
0

==> 2x^2 - 14x + 20 =
0

Now we will divide by
2:

==> x^2 - 7x + 10 =
0

==> ( x - 2) ( x- 5) =
0

==> x1 = 2  ==> y1= 7-2 =
5

==> x2= 5 ==> y2= 7-5 =
2

Then the answer is the
pairs:

( 2, 5) OR ( 5, 2)