Find the solution to the system of equations algebraically. show all work for full credit! x+y=-6 xy=-7

You can solve this by substitution: 

x + y = -6
y = -6-x
Substitute for y in  xy = -7:-
x(-6 - x) = -7
-x^2 - 6x = -7

x^2 + 6x - 7 = 0
(x + 7)(x - 1) = 0

so x = -7, 1

To find the values of y plug  these va;ues of x into the equation x + y = -6:-
when x = -7,  y = -6 + 7 = 1
when x =  1, y = -6 - 1 =  -7

so answer is  x = -7 and y = 1
  and              x = 1 and y = -7

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