Use the elimination method to find all solutions of the system
{x2+y2=8x2−y2=3\displaystyle {\left\lbrace\begin{array}{c} {x}^{{2}}+{y}^{{2}}={8}\\{x}^{{2}}-{y}^{{2}}={3}\end{array}\right.}
The four solutions of the system are:
the one with x<0,y<0\displaystyle {x}<{0},{y}<{0} is
x=\displaystyle {x}=  
y=\displaystyle {y}=  
the one with x<0,y>0\displaystyle {x}<{0},{y}>{0} is
x=\displaystyle {x}=  
y=\displaystyle {y}=  
the one with x>0,y<0\displaystyle {x}>{0},{y}<{0} is
x=\displaystyle {x}=  
y=\displaystyle {y}=  
the one with x>0,y>0\displaystyle {x}>{0},{y}>{0} is
x=\displaystyle {x}=  
y=\displaystyle {y}=  

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