Though @Onuora Chidera got it first but he/she wasn't able to prove to us how they got the answer but Goodness Barak was able to do that, so he gets the cash gift. Congrats.

Making y the subject in equation 2...
y=3+x.....equation 3
Substitute in equation 1...
x²+(3+x)²=29
x²+9+6x+x²=29
2x²+6x-20=0
Using quadratic formula..
x=2 or -5
Substitute in equation 3
When x=2
y=3+2
y=5
When x=-5
y=3+(-5)
Y=-2

x=2 or -5
y = 5 or -2

@Onuora Chidera please show us your steps so that you can get your paymemt.

@Onuora Chidera got it right but it is better you always take us through the process of solving it so others can learn from it. Naitalk is to make knowledge available to people, so while solving you take teacher's seat and guide us.

x=2 y=5