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

justaguide | College Teacher | (Level 2) Distinguished Educator

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We have the following equations to solve for y.

sqrt ( y - 4) = x + 1

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

sqrt ( y - 4) = x + 2

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

from (1) - (2) , we get

y - 4 - y - 4 = x^2 + 2x + 1 - x^2 - 4x - 4

=> -8 = -2x - 3

=> 2x = 5

=> x = 5/2

substituting this in (1)

y - 4 = (5/2)^2 + 2*(5/2) + 1

=> y = (5/2)^2 + 5 + 1 + 4

=> y = 25/4 + 10

=> y = 65/4

Therefore x is 5/2 and y is 65/4.

neela | High School Teacher | (Level 3) Valedictorian

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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.