If $$x^2+xy+x=18$$​ and $$y^2+xy+y=24$$​, then the value of x + y is:

Correct option is C

Given:

​$$x^2 + xy + x = 18$$​​

​$$y^2 + xy + y = 24$$​​

Formula Used:

$$x^2 + 2xy + y^2 = (x + y)^2$$​

Solution:

Adding the two given equations:

factor of  42 could be  =  $$6 \cdot 7 \quad \text{or} \quad -6 \cdot -7$$ 

for fist case; 

​$$(x + y)(x + y + 1) = 6 \times 7$$ 

comparing this we get: 

x + y = 6 

for second case;

​$$(x + y)(x + y + 1) = -7 \times -6$$ 

comparing this we get;

x + y = - 7 

Thus, the value of x + y could be 6 or -7.