System Of equations read the description

Question

y = √x + 7 + 2

y = √ 3 - x

Note x + 7 is under the square root symbol

Note 3 - x is under the square root symbol 

PLEASE HELP

Answer 1

sqrt(x+7) + 2 = sqrt(3-x)

 

 

(x+7) + 2*2*sqrt(x+7) + 4 = 3-x

 

x+11 + 4*Sqrt(x+7) = 3-x

 

4*sqrt(x+7) = 3 - x - x - 11

 

4*Sqrt(x+7) = -2x - 8

 

sqrt(x+7) = (-1/2)(x+4)

 

x+7 = (1/4)(x+4)^2

 

(1/4)(x^2+8x+16) - x - 7 = 0

 

x^2 + 8x + 16 - 4x - 28 = 0

 

x^2 + 4x - 12 = 0

 

( x  +  6)( x  -  2 ) = 0

 

x=-6  or x = 2

 

 

CHECK:

 

X=-6:

  sqrt(-6+7)+2 = sqrt(1) + 2 = 1+2= 3 vs.  sqrt(3 - -6) = sqrt( 9) = 3

 

 

X=2:

 

   sqrt(2+7) = sqrt(9) = 3   vs.  sqrt(3-2) = sqrt(1) = 1

 

The only solution is x=-6