The number of solutions of the system of equations x + y = 49 and y = x^(2) - 3x + 19 is __.__
Given,
x + y = 49....(Equation 1) 
y = x^(2)-3x+19...(Equation 2) 

Substituting the value of y from equation 2 in equation 1, we get
x + x^(2)-3x + 19 = 49
x^(2) - 2x - 30 = 0 
To check if x^(2) - 2x -30 =0 contains a solution from the given options, let's solve this equation, 
x^(2) - 2x - 30 = 0 
We know, (a + b)(a - b) = a^(2) - b^(2) and a^(2) - 2ab + b^(2) = (a - b)^(2)
So, x^(2)-2x - 30 = x^(2)-2x +1 - 31 = (x-1)^(2) - 31 = 0
x^(2)-2x - 30 = (x-1)^(2) - 31 = 0
Now, (x-1) 2 - 31 = 0
x -1±√(1 + 124)/2=0
x -1±√125/2 = 0
As (x -1) -11.1803 = 0 or (x-1)+11.1803=0 
x = 0.1803 or x= -10.1803