Solve the following equations for x and y:1. sqrt(y - 4) = x + 12. sqrt(y + 4) = x + 2

To solve the system of
equations:

sqrt(y - 4)  = x +
1...............(1)
sqrt(y + 4) = x +
2...............(2)

We square the both sides of the
equation (1) and we get:

y-4 =
(x+1)^2.....(1)

We square  both sides of (2) and we get
:

y+4 =
(x+2)^2.....(2).

(2)-(1): 8 = (x+2)^2-(x+1)^2 =
(x+2+x+1)(x+2-(x+1), as (a^2-b^2 = (a+b)(a-b).

=> 8
= 2x+3.

=> 8-3 = 2x.

So
x = 5/2 = 2.5.

Therefore sqrty-4 = (x+1)^2 = 3.5^2 =
12.25.

So y = 12.25+4 =
16.25.

Therefore x= 2.5 and y =
16.25.